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BEGIN:VEVENT
SUMMARY:Lexing Ying (Stanford University)
DTSTART:20200408T231000Z
DTEND:20200409T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/1
DESCRIPTION:Title: Solving inverse problems with deep learning\nby Lexing
Ying (Stanford University) as part of Berkeley applied mathematics seminar
\n\n\nAbstract\nThis talk is about some recent progress on solving inverse
problems using deep learning. Compared to traditional machine learning pr
oblems\, inverse problems are often limited by the size of the training da
ta set. We show how to overcome this issue by incorporating mathematical a
nalysis and physics into the design of neural network architectures. We fi
rst describe neural network representations of pseudodifferential operator
s and Fourier integral operators. We then continue to discuss applications
including electric impedance tomography\, optical tomography\, inverse ac
oustic/EM scattering\, and travel-time tomography.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Mahoney (UC Berkeley)
DTSTART:20200422T231000Z
DTEND:20200423T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/2
DESCRIPTION:Title: Determinantal point processes and randomized numerical line
ar algebra\nby Michael Mahoney (UC Berkeley) as part of Berkeley appli
ed mathematics seminar\n\n\nAbstract\nRandomized Numerical Linear Algebra
(RandNLA) is an area which uses randomness\, most notably random sampling
and random projection methods\, to develop improved algorithms for ubiquit
ous matrix problems\, such as those that arise in scientific computing\, d
ata science\, machine learning\, etc. A seemingly different topic\, but on
e which has a long history in pure and applied mathematics\, is that of De
terminantal Point Processes (DPPs)\, which are stochastic point processes\
, the probability distribution of which is characterized by sub-determinan
ts of some matrix. Recent work has uncovered deep and fruitful connections
between DPPs and RandNLA. For example\, random sampling with a DPP leads
to new kinds of unbiased estimators for classical RandNLA tasks\, enabling
more refined statistical and inferential understanding of RandNLA algorit
hms\; a DPP is\, in some sense\, an optimal randomized method for many Ran
dNLA problems\; and a standard RandNLA technique\, called leverage score s
ampling\, can be derived as the marginal distribution of a DPP. This work
will be reviewed\, as will recent algorithmic developments\, illustrating
that\, while not quite as efficient as simply applying a random projection
\, these DPP-based algorithms are only moderately more expensive. Joint wo
rk with Michal Derezinski.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Kamrin (MIT)
DTSTART:20200429T231000Z
DTEND:20200430T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/3
DESCRIPTION:Title: Toward reduced-order models for flowing grains: Surprising
complexity meets surprising simplicity\nby Ken Kamrin (MIT) as part of
Berkeley applied mathematics seminar\n\n\nAbstract\nDespite the commonali
ty of granular materials in day-to-day life\, modeling systems of millions
or more flowing particles has proven historically difficult. This has dir
ect real-world ramifications owing to the prominent role granular media pl
ay in multiple industries and in terrain dynamics. One can attempt to trac
k every grain with discrete particle methods\, but realistic systems are o
ften too large for this approach and a continuum model is desired. However
\, granular media display unusual behaviors that complicate the continuum
treatment: they can behave like solid\, flow like liquid\, or separate int
o a “gas”\, and the rheology of the flowing state displays remarkable
subtleties.\n\nTo address these challenges\, in this talk we develop a fam
ily of continuum models and solvers\, permitting quantitative modeling cap
abilities. We discuss a variety of applications\, ranging from general pro
blems to specific techniques for problems of intrusion\, impact\, driving\
, and locomotion in granular media. To calculate flows in general cases\,
a rather significant nonlocal effect is evident\, which is well-described
with our recent nonlocal model accounting for grain cooperativity within t
he flow rule. On the other hand\, to model only intrusion forces on submer
ged objects\, we will show\, and explain why\, many of the experimentally
observed results can be captured from a much simpler tension-free friction
al plasticity model. This approach gives way to some surprisingly simple g
eneral tools\, including the granular Resistive Force Theory\, and a broad
set of scaling laws inherent to the problem of granular locomotion. These
scalings are validated directly and suggest a new down-scaled paradigm fo
r granular locomotive design\, on earth and beyond\, to be used much like
scaling laws in fluid mechanics.\n\nWe close with a brief discussion of on
going modeling efforts for wet granular systems\, including those with non
-trivial grain-grain interactions and those with highly deformable particl
es.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kolda (Sandia National Laboratory)
DTSTART:20200506T231000Z
DTEND:20200507T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/4
DESCRIPTION:Title: Practical leverage-based sampling for low-rank tensor decom
position\nby Tamara Kolda (Sandia National Laboratory) as part of Berk
eley applied mathematics seminar\n\n\nAbstract\nConventional algorithms fo
r finding low-rank canonical polyadic (CP) tensor decompositions are unwie
ldy for large sparse tensors. The CP decomposition can be computed by solv
ing a sequence of overdetermined least problems with special Khatri-Rao st
ructure. In this work\, we present an application of randomized algorithms
to fitting the CP decomposition of sparse tensors\, solving a significant
ly smaller sampled least squares problem at each iteration with probabilis
tic guarantees on the approximation errors. Prior work has shown that sket
ching is effective in the dense case\, but the prior approach cannot be ap
plied to the sparse case because a fast Johnson-Lindenstrauss transform (e
.g.\, using a fast Fourier transform) must be applied in each mode\, causi
ng the sparse tensor to become dense. Instead\, we perform sketching throu
gh leverage score sampling\, crucially relying on the fact that the struct
ure of the Khatri-Rao product allows sampling from overestimates of the le
verage scores without forming the full product or the corresponding probab
ilities. Naïve application of leverage score sampling is infective becaus
e we often have cases where a few scores are quite large\, so we propose a
novel hybrid of deterministic and random leverage-score sampling which is
more efficient and effective. Numerical results on real-world large-scale
tensors show the method is faster than competing methods without sacrific
ing accuracy. This is joint work with Brett Larsen at Stanford University.
\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linfeng Zhang (Princeton University)
DTSTART:20200513T231000Z
DTEND:20200514T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/5
DESCRIPTION:Title: Symmetry preserving neural network models for molecular mod
elling\nby Linfeng Zhang (Princeton University) as part of Berkeley ap
plied mathematics seminar\n\n\nAbstract\nWe discuss how to leverage the fi
tting ability of neural networks to accurately and efficiently represent t
wo types of maps in molecular modelling problems. The first type takes as
input the coordinates of atoms and their associated chemical species\, and
outputs physical observables such as the interatomic potential energy (a
scalar)\, the electric polarization (a vector) and polarizability (a tenso
r)\, and the charge density (a field). The second type\, like post–Hartr
ee–Fock methods\, uses the ground-state electronic orbitals as the input
\, and predicts the energy difference between results of highly accurate m
odels such as the coupled-cluster method and low accuracy models such as t
he Hartree-Fock (HF) method. Special attentions are paid to how the neural
network models take care of physical properties like symmetry and localit
y\, so that models trained with small-size systems can be transferred to d
ifferent and large-size ones\; and how they are made end-to-end\, so that
little human intervention is required for various complex tasks. This is j
oint work with Yixiao Chen\, Han Wang\, and Weinan E.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanhe Huang (UC Berkeley)
DTSTART:20200818T231000Z
DTEND:20200819T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/6
DESCRIPTION:Title: Axisymmetric bubbles rising in 3D and a new accurate algori
thm for evaluating orthogonal polynomials\nby Yanhe Huang (UC Berkeley
) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nn the hig
h Reynolds number regime\, under what conditions do there exist steadily r
ising bubbles? This question has been studied extensively both experimenta
lly and numerically\, but current mathematical models and numerical discre
tizations suffer from large numerical errors that make the results less co
nvincing. In the first part of this talk\, we build an inviscid model for
the steady rising problem and find different solution branches of bubble s
hapes characterized by the number of humps. These only exist when there is
no gravity. When there is gravity\, viscous potential flow is used to fin
d different steady shapes. The corresponding dynamic problem is also studi
ed. Techniques such as axisymmetric potential theory\, Hou-Lowengrub-Shell
ey framework\, and weak/hyper-singularity removal are applied to guarantee
spectral accuracy.\n\nDue to the importance of accurate evaluation of ort
hogonal polynomials in the boundary integral method used in the first part
\, in the second part of the talk I will introduce a new way to evaluate o
rthogonal polynomials more accurately near the endpoints of the integratio
n interval. An associated family of orthogonal polynomials is evaluated at
interior points to determine the values of the original polynomials near
endpoints. The new method can achieve round-off error accuracy even for en
d-point evaluation of generic high-degree Jacobi polynomials and generaliz
ed Laguerre polynomials. More accurate quadrature abscissas and weights ca
n be achieved accordingly.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20200826T231000Z
DTEND:20200827T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/7
DESCRIPTION:Title: Solving Linear Systems of Equations via Randomized Kaczmarz
/Stochastic Gradient Descent\nby Stefan Steinerberger (University of W
ashington) as part of Berkeley applied mathematics seminar\n\n\nAbstract\n
The Randomized Kaczmarz method is a classical iterative method to solve li
near systems: the solution of a system Ax = b is simply the point of inter
section of several hyperplanes. The Kaczmarz method (also known as the Pro
jection Onto Convex Sets Method) proceeds by simply starting with a point
and then iteratively projecting it on these hyperplanes. If the hyperplane
s (=rows of the matrix) are picked in random order\, the algorithm was ana
lyzed by Strohmer & Vershynin and has linear convergence. We show that the
method\, as a byproduct\, also computes small singular vectors and\, in f
act\, the iterates tend to approach the true solution from the direction o
f the smallest singular vector in a meta-stable way. This also explains wh
y the algorithm has such wonderful regularization properties. The argument
s are all fairly self-contained\, elementary and nicely geometric. This gi
ves a pretty clear picture – the question is: can this picture be used t
o improve the method?\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Ma (Stanford University)
DTSTART:20200902T231000Z
DTEND:20200903T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/8
DESCRIPTION:Title: The Slow Deterioration of the Generalization Error of the R
andom Feature Model\nby Chao Ma (Stanford University) as part of Berke
ley applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weile Jia (UC Berkeley)
DTSTART:20200909T231000Z
DTEND:20200910T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/9
DESCRIPTION:Title: HPC+AI: pushing ab initio MD to 100 million atoms on the Su
mmit supercomputer\nby Weile Jia (UC Berkeley) as part of Berkeley app
lied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Townsend (Cornell University)
DTSTART:20200916T231000Z
DTEND:20200917T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/10
DESCRIPTION:Title: The ultraspherical spectral method\nby Alex Townsend (
Cornell University) as part of Berkeley applied mathematics seminar\n\n\nA
bstract\nPseudospectral methods\, based on high degree polynomials\, have
spectral accuracy when solving differential equations but typically lead t
o dense and ill-conditioned matrices. The ultraspherical spectral method i
s a numerical technique to solve ordinary and partial differential equatio
ns\, leading to almost banded well-conditioned linear systems while mainta
ining spectral accuracy. In this talk\, we introduce the ultraspherical sp
ectral method and develop it into a spectral element method using a modifi
cation to a hierarchical Poincare-Steklov domain decomposition method.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Bukac (University of Notre Dame)
DTSTART:20200923T231000Z
DTEND:20200924T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/11
DESCRIPTION:Title: A computational framework for fluid-structure interaction
problems\nby Martina Bukac (University of Notre Dame) as part of Berke
ley applied mathematics seminar\n\n\nAbstract\nFluid-structure interaction
(FSI) problems arise in many applications\, such as aerodynamics\, geomec
hanics and hemodynamics. They are moving domain\, multiphysics problems ch
aracterized by nonlinear coupling between a fluid and structure. As a resu
lt\, FSI problems are challenging to numerically solve and analyze. A popu
lar approach is to solve the fluid and structure sub-problems in a partiti
oned manner\, allowing the use of solvers specifically designed for the ph
ysics of each subproblem. However\, stability issues often arise as a resu
lt of FSI coupling unless the design and implementation of a partitioned s
cheme is carefully developed. We will present a family of partitioned nume
rical schemes for the interaction between an incompressible\, viscous flui
d and an elastic structure. We will consider cases where the structure is
thick\, i.e.\, described using the same number of spatial dimensions as th
e fluid\, and when the structure is thin\, i.e.\, described using a lower-
dimensional model. We will present stability and convergence results\, as
well as numerical examples where the presented methods are compared to oth
er methods in the literature.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Childs (University of Maryland)
DTSTART:20200930T231000Z
DTEND:20201001T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/12
DESCRIPTION:Title: Symmetries\, graph properties\, and quantum speedups\n
by Andrew Childs (University of Maryland) as part of Berkeley applied math
ematics seminar\n\n\nAbstract\nAaronson and Ambainis (2009) and Chailloux
(2018) showed that fully symmetric (partial) functions do not admit expone
ntial quantum query speedups. This raises a natural question: how symmetri
c must a function be before it cannot exhibit a large quantum speedup?\n\n
In this work\, we prove that hypergraph symmetries in the adjacency matrix
model allow at most a polynomial separation between randomized and quantu
m query complexities. We also show that\, remarkably\, permutation groups
constructed out of these symmetries are essentially the only permutation g
roups that prevent super-polynomial quantum speedups. We prove this by ful
ly characterizing the primitive permutation groups that allow super-polyno
mial quantum speedups.\n\nIn contrast\, in the adjacency list model for bo
unded-degree graphs (where graph symmetry is manifested differently)\, we
exhibit a property testing problem that shows an exponential quantum speed
up. These results resolve open questions posed by Ambainis\, Childs\, and
Liu (2010) and Montanaro and de Wolf (2013).\n\nThis is joint work with Sh
alev Ben-David\, András Gilyén\, William Kretschmer\, Supartha Podder\,
and Daochen Wang. https://arxiv.org/abs/2006.12760\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franziska Weber (Carnegie Mellon University)
DTSTART:20201014T231000Z
DTEND:20201015T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/13
DESCRIPTION:Title: Numerical approximation of statistical solutions of hyperb
olic systems of conservation laws\nby Franziska Weber (Carnegie Mellon
University) as part of Berkeley applied mathematics seminar\n\n\nAbstract
\nStatistical solutions are time-parameterized probability measures on spa
ces of integrable functions\, which have been proposed recently as a frame
work for global solutions for multi-dimensional hyperbolic systems of cons
ervation laws. We develop a numerical algorithm to approximate statistical
solutions of conservation laws and show that under the assumption of ‘w
eak statistical scaling’\, which is inspired by Kolmogorov’s 1941 turb
ulence theory\, the approximations converge in an appropriate topology to
statistical solutions. Numerical experiments confirm that the assumption m
ight hold true.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rolando Somma (Los Alamos National Laboratory)
DTSTART:20201021T231000Z
DTEND:20201022T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/14
DESCRIPTION:Title: Quantum linear systems problem: solution and verification<
/a>\nby Rolando Somma (Los Alamos National Laboratory) as part of Berkeley
applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dong An (UC Berkeley)
DTSTART:20201028T231000Z
DTEND:20201029T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/15
DESCRIPTION:Title: Quantum adiabatic evolution and applications in computatio
nal physics and quantum computing\nby Dong An (UC Berkeley) as part of
Berkeley applied mathematics seminar\n\n\nAbstract\nOriginally discovered
by Born and Fock (1928)\, a quantum mechanical system almost remains in i
ts instantaneous eigenstates if the Hamiltonian varies sufficiently slowly
and there is a gap between the eigenvalue and the rest of the Hamiltonian
’s spectrum. Such a system is said to be a quantum adiabatic evolution\,
and has become a powerful tool for analyzing quantum dynamics and designi
ng fast classical and quantum algorithms. In this talk\, I will first disc
uss the mathematical formulation of quantum adiabatic evolutions\, namely
quantum adiabatic theorem. Several versions of the theorem will be discuss
ed\, with a focus on the factors that might significantly influence the ad
iabaticity. Then I will present two applications of the adiabatic evolutio
ns and adiabatic theorems. One is accelerating numerical simulation of Sch
rodinger equations on classical computers\, and the other is a quantum alg
orithm for solving linear system of equations with near optimal complexity
on a quantum computer.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaochuan Tian (UCSD)
DTSTART:20201105T001000Z
DTEND:20201105T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/16
DESCRIPTION:Title: Reproducing kernel collocation methods for nonlocal models
: asymptotic compatibility and numerical stability\nby Xiaochuan Tian
(UCSD) as part of Berkeley applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiequn Han (Princeton University)
DTSTART:20201112T001000Z
DTEND:20201112T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/17
DESCRIPTION:Title: Solving High-Dimensional PDEs\, Controls\, and Games with
Deep Learning\nby Jiequn Han (Princeton University) as part of Berkele
y applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Webber (Courant Institute)
DTSTART:20201203T001000Z
DTEND:20201203T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/18
DESCRIPTION:Title: Monte Carlo methods for the Hermitian eigenvalue problem\nby Robert Webber (Courant Institute) as part of Berkeley applied mathe
matics seminar\n\n\nAbstract\nIn quantum mechanics and the analysis of Mar
kov processes\, Monte Carlo methods are needed to identify low-lying eigen
functions of dynamical generators. The standard Monte Carlo approaches for
identifying eigenfunctions\, however\, can be inaccurate or slow to conve
rge. What limits the efficiency of the currently available spectral estima
tion methods\, and what is needed to build more efficient methods for the
future? Through numerical analysis and computational examples\, we begin t
o answer these questions. We present the first-ever convergence proof and
error bounds for the variational approach to conformational dynamics (VAC)
\, the dominant method for estimating eigenfunctions used in biochemistry.
Additionally\, we analyze and optimize variational Monte Carlo (VMC)\, wh
ich combines Monte Carlo with neural networks to accurately identify low-l
ying eigenstates of quantum systems.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aditi Krishnapriyan (Lawrence Berkeley National Lab)
DTSTART:20201007T231000Z
DTEND:20201008T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/19
DESCRIPTION:Title: Persistent Homology Advances Interpretable Machine Learnin
g for Scientific Applications\nby Aditi Krishnapriyan (Lawrence Berkel
ey National Lab) as part of Berkeley applied mathematics seminar\n\n\nAbst
ract\nMachine learning for scientific applications\, ranging from physics
and materials science to biology\, has emerged as a promising alternative
to more time-consuming experiments and simulations. The challenge with thi
s approach is the selection of features that enable universal and interpre
table system representations across multiple prediction tasks. We use pers
istent homology to construct holistic feature representations to describe
the structure of scientific systems\; for example\, material and protein s
tructures. We show that these representations can also be augmented with o
ther generic features to capture further information. We demonstrate our a
pproaches on multiple scientific datasets by predicting a variety of diffe
rent targets across different conditions. Our results show considerable im
provement in both accuracy and transferability across targets compared to
models constructed from commonly used manually curated features. A key adv
antage of our approach is interpretability. For example\, in material stru
ctures\, our persistent homology features allow us to identify the locatio
n and size of pores in the structure that correlate best to different mate
rials properties\, contributing to understanding atomic level structure-pr
operty relationships for materials design.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Stokes (Flatiron Institute)
DTSTART:20201119T001000Z
DTEND:20201119T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/20
DESCRIPTION:Title: First-quantized neural networks for lattice fermions\n
by James Stokes (Flatiron Institute) as part of Berkeley applied mathemati
cs seminar\n\n\nAbstract\nFirst-quantized deep neural network techniques a
re developed for analyzing strongly coupled fermionic systems on the latti
ce. Using a Slater-Jastrow inspired ansatz which exploits deep residual ne
tworks with convolutional residual blocks\, we approximately determine the
ground state of spinless fermions on a square lattice with nearest-neighb
or interactions. The flexibility of the neural-network ansatz results in a
high level of accuracy when compared to exact diagonalization results on
small systems\, both for energy and correlation functions. On large system
s\, we obtain accurate estimates of the boundaries between metallic and ch
arge ordered phases as a function of the interaction strength and the part
icle density.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongbin Xiu (The Ohio State University)
DTSTART:20210211T001000Z
DTEND:20210211T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/21
DESCRIPTION:by Dongbin Xiu (The Ohio State University) as part of Berkeley
applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seung-Yeal Ha (Seoul National University)
DTSTART:20210428T231000Z
DTEND:20210429T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/23
DESCRIPTION:Title: Emergent behaviors of Lohe tensor flocks\nby Seung-Yea
l Ha (Seoul National University) as part of Berkeley applied mathematics s
eminar\n\n\nAbstract\nIn this talk\, we present a new aggregation model on
the space of rank-m tensors with the same size\, and study emergent dynam
ics of the proposed model. Our proposed aggregation model is general enoug
h to include Lohe type synchronization models such as the Kuramoto model\,
the Lohe sphere model and the Lohe matrix models for the ensemble of real
rank-0\, rank-1 and rank-2 tensors\, respectively. In this regard\, we ca
ll our proposed model as the Lohe tensor model for rank-m tensors with the
same size. For the proposed model\, we present several sufficient framewo
rks leading to the collective dynamics of the Lohe tensor model in terms o
f system parameters and initial data\, and study existence of special solu
tions such as completely separable solutions and quadratically separable s
olutions. This is a joint work with Hansol Park (Seoul National Univ.) an
d Dohyun Kim (Sungshin Women’s Univ.)\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianfeng Lu (Duke University)
DTSTART:20210204T001000Z
DTEND:20210204T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/24
DESCRIPTION:Title: Towards solving high dimensional PDEs using neural network
s\nby Jianfeng Lu (Duke University) as part of Berkeley applied mathem
atics seminar\n\n\nAbstract\nNumerical solution to high dimensional PDEs h
as been one of the central challenges in scientific computing due to curse
of dimension. In recent years\, we have seen tremendous progress in apply
ing neural networks to solve high dimensional PDEs\, while the analysis fo
r such methods is still lacking. In this talk\, we will discuss some of th
ese numerical methods for high dimensional PDEs and also some initial atte
mpts in numerical analysis for high dimensional PDEs.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doron Levy (University of Maryland)
DTSTART:20210304T001000Z
DTEND:20210304T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/25
DESCRIPTION:Title: Fighting drug resistance with math\nby Doron Levy (Uni
versity of Maryland) as part of Berkeley applied mathematics seminar\n\n\n
Abstract\nThe emergence of drug-resistance is a major challenge in chemoth
erapy. In this talk we will overview some of our recent mathematical model
s for describing the dynamics of drug-resistance in solid tumors. These mo
dels follow the dynamics of the tumor\, assuming that the cancer cell popu
lation depends on a phenotype variable that corresponds to the resistance
level to a cytotoxic drug. Under certain conditions\, our models predict
that multiple resistant traits emerge at different locations within the tu
mor\, corresponding to heterogeneous tumors. We show that a higher drug do
sage may delay a relapse\, yet\, when this happens\, a more resistant trai
t emerges. We will show how mathematics can be used to propose an efficien
t drug schedule aiming at minimizing the growth rate of the most resistant
trait\, and how such resistant cells can be eliminated.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruiwen Shu (University of Maryland\, College Park)
DTSTART:20210128T001000Z
DTEND:20210128T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/26
DESCRIPTION:Title: Linear interpolation convexity/concavity in the minimizati
on of attractive-repulsive energy\nby Ruiwen Shu (University of Maryla
nd\, College Park) as part of Berkeley applied mathematics seminar\n\n\nAb
stract\nEnergy minimization problems of attractive-repulsive pairwise inte
ractions are very important in the study of pattern formation in biologica
l and social sciences. In this talk\, I will discuss some recent progress
(joint work with Jose Carrillo) on the study of Wasserstein-$\\infty$ loca
l energy minimizers by using the method of linear interpolation convexity/
concavity. In the first part\, we prove the radial symmetry and uniqueness
of local minimizers for interaction potentials satisfying the 'linear int
erpolation convexity'\, which generalizes the result of O. Lopes 17' for g
lobal minimizers. In the second part\, we show that the failure of linear
interpolation convexity could lead to the formation of small scales in the
support of local minimizers\, and construct interaction potentials whose
local minimizers are supported on fractal sets. To our best knowledge\, th
is is the first time people observe fractal sets as the support of local m
inimizers.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitchell Luskin (University of Minnesota)
DTSTART:20210331T231000Z
DTEND:20210401T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/27
DESCRIPTION:Title: Mathematics and Physics at the Moiré Scale\nby Mitche
ll Luskin (University of Minnesota) as part of Berkeley applied mathematic
s seminar\n\n\nAbstract\nPlacing a two-dimensional lattice on another with
a small rotation gives rise to periodic “moire” patterns on a superla
ttice scale much larger than the original lattice. This effective large-sc
ale fundamental domain allows phenomena such as the fractal Hofstadter but
terfly in the spectrum of Harper’s equation to be observed in real cryst
als. Experimentalists have more recently observed new correlated phases at
the “magic” twist angles predicted by theorists. \n\nWe will give mat
hematical and computational models to predict and gain insight into new ph
ysical phenomena at the moiré scale including our recent mathematical and
experimental results for twisted trilayer graphene.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Horning (Cornell University)
DTSTART:20210121T001000Z
DTEND:20210121T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/28
DESCRIPTION:Title: Computing spectral properties of infinite-dimensional oper
ators\nby Andrew Horning (Cornell University) as part of Berkeley appl
ied mathematics seminar\n\n\nAbstract\nComputing the spectrum of a differe
ntial or integral operator is usually done in two steps: (1) discretize th
e operator to obtain a matrix eigenvalue problem and (2) compute eigenvalu
es of the matrix with numerical linear algebra. This “discretize-then-so
lve” paradigm is flexible and powerful\, but tension between spectral pr
operties of the operator and the matrix discretizations can lead to numeri
cal artifacts that pollute computed spectra and degrade accuracy. Moreover
\, it is unclear how to robustly capture infinite-dimensional phenomena\,
like continuous spectra\, with “discretize-then-solve.” In this talk\,
we introduce a new computational framework that extracts discrete and con
tinuous spectral properties of a broad class of operators by strategically
sampling the resolvent operator in the complex plane. The resulting algor
ithms respect key structure from the operator\, regardless of the underlyi
ng matrix discretizations used for computation. We illustrate the approach
through a range of examples\, including a Dirac operator and a magnetic t
ight-binding model of graphene.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhewei Yao (University of California\, Berkeley)
DTSTART:20210218T001000Z
DTEND:20210218T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/29
DESCRIPTION:Title: Second Order Methods for Neural Network Analysis\, Trainin
g\, and Inference\nby Zhewei Yao (University of California\, Berkeley)
as part of Berkeley applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenning Cai (National University of Singapore)
DTSTART:20210225T001000Z
DTEND:20210225T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/30
DESCRIPTION:Title: On the method of complex Langevin\nby Zhenning Cai (Na
tional University of Singapore) as part of Berkeley applied mathematics se
minar\n\n\nAbstract\nThe complex Langevin (CL) method is a numerical appro
ach to alleviate the numerical sign problem in the computation of path int
egrals in lattice field theories. Mathematically\, it is a simple numerica
l tool to compute a wide class of high-dimensional and oscillatory integra
ls with the form of an ensemble average. The method was developed in 1980s
. However\, after it was proposed\, it had very few applications due to it
s subtle nature. It is often observed that the CL method converges but the
limiting result is incorrect. Less than one decade ago\, the CL method wa
s improved by gauge cooling method and dynamical stabilization\, after whi
ch the CL method acquired much more attention and was later successfully a
pplied to a number of fields including finite density quantum chromodynami
cs\, superstring theory\, and the spin-orbit coupling. In this talk\, I wi
ll take the mathematical perspective to explain the basic idea of the CL m
ethod and the reason of its failure. The current limitation of the method
and the possible remedies will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Casas (Universitat Jaume I\, Spain)
DTSTART:20210311T001000Z
DTEND:20210311T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/31
DESCRIPTION:Title: Symmetric-conjugate composition methods in the numerical i
ntegration of differential equations\nby Fernando Casas (Universitat J
aume I\, Spain) as part of Berkeley applied mathematics seminar\n\n\nAbstr
act\nIn this talk I will analyze composition methods with complex coeffici
ents exhibiting the so-called “symmetry-conjugate” pattern in their di
stribution. In particular\, I will study their behavior with respect to pr
eservation of qualitative properties when projected on the real axis and h
ow they compare with the usual left-right palindromic compositions. New sc
hemes within this family up to order 8 will be proposed and illustrated on
several examples. Some of the special features of this class of methods w
ill also be reviewed.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuan Su (Caltech)
DTSTART:20210319T171000Z
DTEND:20210319T180000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/32
DESCRIPTION:Title: Nearly tight Trotterization of interacting electrons\n
by Yuan Su (Caltech) as part of Berkeley applied mathematics seminar\n\n\n
Abstract\nWe consider simulating quantum systems on digital quantum comput
ers. We show that the performance of quantum simulation can be improved by
simultaneously exploiting the commutativity of Hamiltonian\, the sparsity
of interactions\, and the prior knowledge of initial state. We achieve th
is using Trotterization for a class of interacting electrons that encompas
ses various physical systems\, including the plane-wave-basis electronic s
tructure and the Fermi-Hubbard model. We estimate the simulation error by
taking the transition amplitude of nested commutators of Hamiltonian terms
within the $\\eta$-electron manifold. We develop multiple techniques for
bounding the transition amplitude and expectation of general fermionic ope
rators\, which may be of independent interest. We show that it suffices to
use $\\left(\\frac{n^{5/3}}{\\eta^{2/3}}+n^{4/3}\\eta^{2/3}\\right)n^{o(1
)}$ gates to simulate electronic structure in the plane-wave basis with $n
$ spin orbitals and $\\eta$ electrons\, improving the best previous result
in second quantization while outperforming the first-quantized simulation
when $n=\\eta^{2-o(1)}$. We also obtain an improvement for simulating the
Fermi-Hubbard model. We construct concrete examples for which our bounds
are almost saturated\, giving a nearly tight Trotterization of interacting
electrons.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jimmy Xia (University of California\, Berkeley)
DTSTART:20210407T231000Z
DTEND:20210408T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/33
DESCRIPTION:Title: Mathematical modeling of human learning and decision makin
g\nby Jimmy Xia (University of California\, Berkeley) as part of Berke
ley applied mathematics seminar\n\n\nAbstract\nReinforcement learning (RL)
has been widely used to study and model human\, animal and artificial int
elligence. In this talk\, we focus on modeling human learning and decision
making\, and exemplify two ways that mathematical RL modeling adds to our
existing knowledge of human cognition: (1) as a powerful quantitative too
l for parametrizing and compressing individual differences in human behavi
or\, and (2) as an important theoretical framework for complex human cogni
tion. In the first study\, we use RL modeling to capture trial-by-trial le
arning dynamics in a probabilistic task and to understand how learning cha
nges during puberty. In the second study\, we augment existing RL models t
o explain transfer and generalization effects in multi-step learning and d
ecision making tasks.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhennan Zhou (Peking University)
DTSTART:20210414T231000Z
DTEND:20210415T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/34
DESCRIPTION:Title: Efficient Sampling of Thermal Averages of Interacting Quan
tum Particle Systems: preconditioning and simulation with random batches\nby Zhennan Zhou (Peking University) as part of Berkeley applied mathem
atics seminar\n\n\nAbstract\nWe investigate the continuum limit that the n
umber of beads goes to infinity in the ring polymer representation of ther
mal averages. Studying the continuum limit of the trajectory sampling equa
tion sheds light on possible preconditioning techniques for sampling ring
polymer configurations with large number of beads. In the case where the p
otential is quadratic\, we show that the continuum limit of the preconditi
oned mass modified Langevin dynamics converges to its equilibrium exponent
ially fast\, which suggests that the finite-dimensional counterpart has a
dimension-independent convergence rate. In the second part of the talk\, a
n efficient sampling method\, the pmmLang+RBM\, is proposed to compute the
quantum thermal average in the interacting quantum particle system. Benef
iting from the random batch method (RBM)\, the pmmLang+RBM reduces the com
plexity due to the interaction forces per timestep from O(NP^2) to O(NP)\,
where N is the number of beads and P is the number of particles. We also
propose an extension of the pmmLang+RBM\, which is based on the splitting
Monte Carlo method and is applicable when the interacting potential contai
ns a singular part.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phillip Colella (Lawrence Berkeley National Laboratory and UC Berk
eley)
DTSTART:20210421T231000Z
DTEND:20210422T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/35
DESCRIPTION:Title: Numerical Analysis of Particle-in-Cell Methods for Advecti
on-Type Partial Differential Equations\nby Phillip Colella (Lawrence B
erkeley National Laboratory and UC Berkeley) as part of Berkeley applied m
athematics seminar\n\n\nAbstract\nParticle-in-cell (PIC) methods for advec
tion equations use particles that move along integral curves of the advect
ion velocity to represent the primary dependent variables\, while using a
structured grid to which the particle state has been interpolated to compu
te the dependence of the velocities\, and forcing terms on the solution.
PIC is one of the oldest methods in numerical PDE\, dating back to the 195
0s for fluid dynamics\, and the 1960s for plasma physics\, and are still u
sed extensively today. Nonetheless\, there appears to be no mathematically
-systematic numerical analysis framework for understanding the error in PI
C methods. This is in contrast to traditional finite-difference\, finite e
lement\, and grid-free particle methods\, for which such framework exist a
nd are used very successfully to design methods for complex problems. In t
his talk\, we will present such a numerical analysis framework for both ad
vection and for kinetics problems. One of the principal results is that PI
C methods\, as they are currently used in scientific applications\, have a
n O(1) contribution to the error\, relative to the number of particles\, t
hat grows exponentially in time. We will describe the source of this error
\, and strategies for controlling it.\n\nJoint work with Henry Boateng\, B
havna Singh\, Erick Velez\, and Colin Wahl.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Hou (Caltech)
DTSTART:20210901T231000Z
DTEND:20210902T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/36
DESCRIPTION:Title: Potential singularity of 3D incompressible Euler equations
and the nearly singular behavior of 3D Navier-Stokes equations\nby Th
omas Hou (Caltech) as part of Berkeley applied mathematics seminar\n\n\nAb
stract\nWhether the 3D incompressible Euler and Navier-Stokes equations ca
n develop a finite time singularity from smooth initial data is one of the
most challenging problems in nonlinear PDEs. In an effort to provide a ri
gorous proof of the potential Euler singularity revealed by Luo-Hou's comp
utation\, we develop a novel method of analysis and prove that the origina
l De Gregorio model and the Hou-Lou model develop a finite time singularit
y from smooth initial data. Using this framework and some techniques from
Elgindi's recent work on the Euler singularity\, we prove the finite time
blowup of the 2D Boussinesq and 3D Euler equations with $C^{1\,\\alpha}$ i
nitial velocity and boundary. Further\, we present some new numerical evid
ence that the 3D incompressible Euler equations with smooth initial data d
evelop a potential finite time singularity at the origin\, which is quite
different from the Luo-Hou scenario. Our study also shows that the 3D Navi
er-Stokes equations develop nearly singular solutions with maximum vortici
ty increasing by a factor of $10^7$. However\, the viscous effect eventual
ly dominates vortex stretching and the 3D Navier-Stokes equations narrowly
escape finite time blowup. Finally\, we present strong numerical evidence
that the 3D Navier-Stokes equations with slowly decaying viscosity develo
p a finite time singularity.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Kuan (UC Berkeley)
DTSTART:20210908T231000Z
DTEND:20210909T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/37
DESCRIPTION:Title: A stochastic fluid-structure interaction problem describin
g Stokes flow interacting with a membrane\nby Jeffrey Kuan (UC Berkele
y) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nIn this
talk\, we present a well-posedness result for a stochastic fluid-structure
interaction model. We study a fully coupled stochastic fluid-structure in
teraction problem\, with linear coupling between Stokes flow and an elasti
c structure modeled by the wave equation\, and stochastic noise in time ac
ting on the structure. Such stochasticity is of interest in applications o
f fluid-structure interaction\, in which there is random noise present whi
ch may affect the dynamics and statistics of the full system. We construct
a solution by using a new splitting method for stochastic fluid-structure
interaction\, and probabilistic methods. To the best of our knowledge\, t
his is the first result on well-posedness for fully coupled stochastic flu
id-structure interaction. This is joint work with Sunčica Čanić (UC Ber
keley).\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Komarova (UC Irvine)
DTSTART:20210915T231000Z
DTEND:20210916T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/38
DESCRIPTION:Title: Mathematical methods in cancer dynamics\nby Natalia Ko
marova (UC Irvine) as part of Berkeley applied mathematics seminar\n\n\nAb
stract\nEvolutionary dynamics are at the core of carcinogenesis. Mathemati
cal methods can be used to study evolutionary processes\, such as selectio
n and mutation\, and to shed light onto cancer origins\, progression\, and
mechanisms of treatment. I will present two broad approaches to cancer mo
deling that we have developed. One is concerned with near-equilibrium dyna
mics of stem cells\, with the goal of figuring out how tissue cell turnove
r is orchestrated\, and how control networks prevent “selfish” cell gr
owth. The other direction is studying evolutionary dynamics of drug resist
ance in cancer.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lindsey (Courant Institute)
DTSTART:20210922T231000Z
DTEND:20210923T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/39
DESCRIPTION:Title: Embedding approaches for classical and quantum statistical
mechanics\nby Michael Lindsey (Courant Institute) as part of Berkeley
applied mathematics seminar\n\n\nAbstract\nWe show how a synthesis of ide
as from graphical models\, tensor networks\, optimal transport\, and semid
efinite programming can be brought to bear on problems from classical and
quantum statistical mechanics\, broadly construed. Specifically\, we discu
ss applications including classical and quantum spin systems on the lattic
e\, continuous global optimization\, and electronic structure.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Becker (University of Cambridge)
DTSTART:20210929T231000Z
DTEND:20210930T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/40
DESCRIPTION:Title: Mathematical properties of twisted bilayer graphene\nb
y Simon Becker (University of Cambridge) as part of Berkeley applied mathe
matics seminar\n\n\nAbstract\nTwistronics is the study of how the angle (t
he twist) between layers of two-dimensional materials can change their ele
ctronic structure. When two sheets of graphene are twisted by those angles
the resulting material exhibits flat bands which\, as argued in the physi
cs literature\, is related to superconductivity\, ferromagnetism\, and Mot
t-insulators. I will start with a very simple operator whose spectral prop
erties are supposed to determine which angles are magical and describe som
e of the mathematical challenges and results. Then\, I will introduce a me
thod to study the response of this material to an external magnetic field
in a regime of large magnetic fields and explain some of the phenomena. Fi
nally\, I will move on to even simpler one-dimensional models\, that natur
ally appear when strain is applied in one direction of the van der Waals m
aterial to make it periodic in one spatial direction\, which allow for a m
ore refined mathematical analysis (Cantor spectrum and metal/insulator tra
nsitions). If time permits\, I will briefly touch upon the connection betw
een such materials and topological insulators.\n\nThis is joint work with
M Embree\, R Kim\, J Wittsten\, X Zhu\, M Zworski.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Gull (University of Michigan)
DTSTART:20211020T231000Z
DTEND:20211021T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/41
DESCRIPTION:Title: Nevanlinna Analytical Continuation\nby Emanuel Gull (U
niversity of Michigan) as part of Berkeley applied mathematics seminar\n\n
\nAbstract\nSimulations of finite temperature quantum systems provide imag
inary frequency Green’s functions that correspond one-to-one to experime
ntally measurable real-frequency spectra. However\, due to the bad conditi
oning of the continuation transform from imaginary to real frequencies\, e
stablished methods tend to either wash out spectral features at high frequ
encies or produce spectral functions with unphysical negative parts. Here\
, we show that explicitly respecting the analytic ‘Nevanlinna' structure
of the Green’s function leads to intrinsically positive and normalized
spectral functions and we present a continued fraction expansion that yiel
ds all possible functions consistent with the analytic structure. Applicat
ion to synthetic trial data shows that sharp\, smooth\, and multi-peak dat
a is resolved accurately. Application to the band structure of silicon dem
onstrates that high energy features are resolved precisely. Continuations
in a realistic correlated setup reveal additional features that were previ
ously unresolved. By substantially increasing the resolution of the real f
requency calculations\, our work overcomes one of the main limitations of
finite-temperature quantum simulations.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Song Mei (UC Berkeley)
DTSTART:20211027T181000Z
DTEND:20211027T190000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/42
DESCRIPTION:Title: The efficiency of kernel methods on structured datasets\nby Song Mei (UC Berkeley) as part of Berkeley applied mathematics semin
ar\n\n\nAbstract\nInspired by the proposal of tangent kernels of neural ne
tworks (NNs)\, a recent research line aims to design kernels with a better
generalization performance on standard datasets. Indeed\, a few recent wo
rks showed that certain kernel machines perform as well as NNs on certain
datasets\, despite their separations in specific cases implied by theoreti
cal results. Furthermore\, it was shown that the induced kernels of convol
utional neural networks perform much better than any former handcrafted ke
rnels. These empirical results pose a theoretical challenge to understandi
ng the performance gaps in kernel machines and NNs in different scenarios.
\n\nIn this talk\, we show that data structures play an essential role in
inducing these performance gaps. We consider a few natural data structures
\, and study their effects on the performance of these learning methods. B
ased on a fine-grained high dimensional asymptotics framework of analyzing
random features models and kernel machines\, we show the following: 1) If
the feature vectors are nearly isotropic\, kernel methods suffer from the
curse of dimensionality\, while NNs can overcome it by learning the best
low-dimensional representation\; 2) If the feature vectors display the sam
e low-dimensional structure as the target function (the spiked covariates
model)\, this curse of dimensionality becomes milder\, and the performance
gap between kernel methods and NNs become smaller\; 3) On datasets that d
isplay some invariance structure (e.g.\, image dataset)\, there is a quant
itative performance gain of using invariant kernels (e.g.\, convolutional
kernels) over inner product kernels. Beyond explaining the performance gap
s\, these theoretical results can further provide some intuitions towards
designing kernel methods with better performance.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Kaye (Flatiron institute)
DTSTART:20211111T001000Z
DTEND:20211111T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/43
DESCRIPTION:Title: Efficient numerical algorithms for simulating quantum dyna
mics\nby Jason Kaye (Flatiron institute) as part of Berkeley applied m
athematics seminar\n\n\nAbstract\nI will describe a few new algorithms whi
ch reduce computational bottlenecks in simulations of quantum many-body dy
namics.\n\nIn time-dependent density functional theory (TDDFT)\, the many-
body wavefunction is approximated using a collection of single-particle wa
vefunctions\, which independently satisfy the Schrodinger equation and are
coupled through an effective potential. I will introduce a high-order\, F
FT-based solver for free space (nonperiodic) problems in TDDFT which sides
teps the usual requirement of imposing artificial boundary conditions.\n\n
Many-body Green's functions\, which describe correlations between quantum
observables\, enable practical simulations beyond the effective one-body p
icture of TDDFT. The Green's functions satisfy history dependent Volterra
integro-differential equations with kernel nonlinearities. I will outline
efficient history integration algorithms which significantly extend feasib
le propagation times in both equilibrium and nonequilibrium calculations.\
n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Chorin (UC Berkeley and LBNL)
DTSTART:20211209T001000Z
DTEND:20211209T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/44
DESCRIPTION:by Alexandre Chorin (UC Berkeley and LBNL) as part of Berkeley
applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Tong (UC Berkeley)
DTSTART:20211103T231000Z
DTEND:20211104T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/45
DESCRIPTION:Title: Quantum eigenstate filtering and its applications\nby
Yu Tong (UC Berkeley) as part of Berkeley applied mathematics seminar\n\n\
nAbstract\nIn this talk I will introduce a quantum algorithmic technique c
alled quantum eigenstate filtering\, which is based on approximation theor
y results and the quantum singular value transformation. I will discuss it
s applications in preparing eigenstates\, solving quantum linear systems\,
and estimating the ground state energy. For these tasks this technique le
ads to significantly better query complexities\, fewer ancilla qubits\, an
d does so without requiring complex subroutines that may not be realistica
lly implementable. Besides these algorithmic applications\, the essential
idea also leads to a useful proof technique for studying the ground state
property of quantum many-body systems.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Di Fang (UC Berkeley)
DTSTART:20211006T231000Z
DTEND:20211007T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/46
DESCRIPTION:Title: Time-dependent unbounded Hamiltonian simulation with vecto
r norm scaling\nby Di Fang (UC Berkeley) as part of Berkeley applied m
athematics seminar\n\n\nAbstract\nHamiltonian simulation is a basic task i
n quantum computation. The accuracy of such simulation is usually measured
by the error of the unitary evolution operator in the operator norm\, whi
ch in turn depends on certain norm of the Hamiltonian. For unbounded opera
tors\, after suitable discretization\, the norm of the Hamiltonian can be
very large\, which significantly increases the simulation cost. However\,
the operator norm measures the worst-case error of the quantum simulation\
, while practical simulation concerns the error with respect to a given in
itial vector at hand. We demonstrate that under suitable assumptions of th
e Hamiltonian and the initial vector\, if the error is measured in terms o
f the vector norm\, the computational cost may not increase at all as the
norm of the Hamiltonian increases using Trotter type methods. In this sens
e\, our result outperforms all previous error bounds in the quantum simula
tion literature. We also clarify the existence and the importance of commu
tator scalings of Trotter and generalized Trotter methods for time-depende
nt Hamiltonian simulations.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franziska Weber (Carnegie Mellon University)
DTSTART:20211013T231000Z
DTEND:20211014T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/47
DESCRIPTION:Title: A Convergent Numerical Method for a Model of Liquid Crysta
l Director Coupled to An Electric Field\nby Franziska Weber (Carnegie
Mellon University) as part of Berkeley applied mathematics seminar\n\n\nAb
stract\nStarting from the Oseen-Frank theory\, we derive a simple model fo
r the dynamics of a nematic liquid crystal director field under the influe
nce of an electric field. The resulting nonlinear system of partial differ
ential equations consists of the electrostatics equations for the electric
field coupled with the damped wave map equation for the evolution of the
liquid crystal director field\, which is a normal vector pointing in the d
irection of the main orientation of the liquid crystal molecules. The liqu
id crystal director field enters the electrostatics equations in the const
itutive relations while the electric field enters the wave map equation in
the form of a nonlinear source term. Since it is a normal vector\, the va
riable for the liquid crystal director field has to satisfy the constraint
that it takes values in the unit sphere. We derive an energy-stable and c
onstraint preserving numerical method for this system and prove convergenc
e of a subsequence of approximations to a weak solution of the system of p
artial differential equations. In particular\, this implies the existence
of weak solutions for this model.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aditi Krishnapriyan (Lawrence Berkeley National Lab)
DTSTART:20211202T001000Z
DTEND:20211202T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/48
DESCRIPTION:Title: Integrating machine learning with physics-based spatial an
d temporal modeling\nby Aditi Krishnapriyan (Lawrence Berkeley Nationa
l Lab) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nDeep
learning has achieved great success in numerous areas\, and is also seein
g increasing interest in scientific applications. However\, challenges sti
ll remain: scientific phenomena are difficult to model\, and can also be l
imited by a lack of training data. As a result\, scientific machine learni
ng approaches are being developed by incorporating domain knowledge into t
he machine learning process to enable more accurate and general prediction
s. One such popular approach\, colloquially known as physics-informed neur
al networks (PINNs)\, incorporates domain knowledge as soft constraints on
an empirical loss function. I will discuss the challenges associated with
such an approach\, and show that by changing the learning paradigm to cur
riculum regularization or sequence-to-sequence learning\, we can achieve s
ignificantly lower error. Another approach\, colloquially known as ODE-Net
s\, aims to couple dynamical systems/numerical methods with neural network
s. I will discuss how exploiting techniques from numerical analysis for th
ese systems can enable learning continuous dynamics for scientific problem
s. This method will be illustrated by showing that it can: resolve fine-sc
ale features in a temporal solution despite training on coarse data\, succ
essfully resolve fine-scale features in the temporal solution even when th
e training data is irregularly spaced with non-uniform time intervals\, an
d learn dynamics from image snapshots by generating super-resolution video
s at higher frame rates of the much finer solution.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No seminar
DTSTART:20220127T001000Z
DTEND:20220127T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/49
DESCRIPTION:by No seminar as part of Berkeley applied mathematics seminar\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Chertock (North Carolina State University)
DTSTART:20220203T001000Z
DTEND:20220203T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/50
DESCRIPTION:Title: Structure Preserving Numerical Methods for Hyperbolic Syst
ems of Conservation and Balance Laws\nby Alina Chertock (North Carolin
a State University) as part of Berkeley applied mathematics seminar\n\n\nA
bstract\nMany physical models\, while quite different in nature\, can be d
escribed by nonlinear hyperbolic systems of conservation and balance laws.
The main source of difficulties one comes across when numerically solving
these systems is lack of smoothness as solutions of hyperbolic conservati
on/balance laws may develop very complicated nonlinear wave structures inc
luding shocks\, rarefaction waves and contact discontinuities. The level o
f complexity may increase even further when solutions of the hyperbolic sy
stem reveal a multiscale character and/or the system includes additional t
erms such as friction terms\, geometrical terms\, nonconservative products
\, etc.\, which are needed to be taken into account in order to achieve a
proper description of the studied physical phenomena. In such cases\, it i
s extremely important to design a numerical method that is not only consis
tent with the given PDEs\, but also preserves certain structural and asymp
totic properties of the underlying problem at the discrete level. While a
variety of numerical methods for such models have been successfully develo
ped\, there are still many open problems\, for which the derivation of rel
iable high-resolution numerical methods still remains to be an extremely c
hallenging task.\n\nIn this talk\, I will discuss recent advances in the d
evelopment of two classes of structure preserving numerical methods for no
nlinear hyperbolic systems of conservation and balance laws. In particular
\, I will present (i) well-balanced and positivity preserving numerical sc
hemes\, that is\, the methods which are capable of exactly preserving some
steady-state solutions as well as maintaining the positivity of the numer
ical quantities when it is required by the physical application\, and (ii)
asymptotic preserving schemes\, which provide accurate and efficient nume
rical solutions in certain stiff and/or asymptotic regimes of physical int
erest.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunan Yang (ETH Zurich)
DTSTART:20220209T181000Z
DTEND:20220209T190000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/51
DESCRIPTION:Title: Adjoint DSMC Method for Boltzmann-Constrained Optimization
Problems\nby Yunan Yang (ETH Zurich) as part of Berkeley applied math
ematics seminar\n\n\nAbstract\nApplications for kinetic equations such as
optimal design and inverse problems often involve finding unknown paramete
rs through gradient-based optimization algorithms. Based on the adjoint-st
ate method\, we derive two different frameworks for approximating the grad
ient of an objective functional constrained by the nonlinear Boltzmann equ
ation. While the forward problem can be solved by the Direct Simulation Mo
nte Carlo (DSMC) method\, it is difficult to efficiently solve the high-di
mensional continuous adjoint equation obtained by the "optimize-then-discr
etize" approach. This challenge motivates us to propose an adjoint DSMC me
thod following the "discretize-then-optimize" approach for Boltzmann-const
rained optimization. We also analyze the properties of the two frameworks
and their connections. Several numerical examples are presented to demonst
rate their accuracy and efficiency.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Laestadius (Hylleraas Centre for Quantum Molecular Sciences)
DTSTART:20220224T001000Z
DTEND:20220224T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/52
DESCRIPTION:Title: Energy error estimate for coupled-cluster excited states\nby Andre Laestadius (Hylleraas Centre for Quantum Molecular Sciences)
as part of Berkeley applied mathematics seminar\n\n\nAbstract\nIn our rece
nt work\, the nonlinear equations of the single-reference Coupled-Cluster
method have been analyzed using topological degree theory. This generalize
s previous work based on (local) strong monotonicity. We have established
existence results and qualitative information about the solutions of these
equations that also sheds light on some of the numerically observed behav
ior. In particular\, to investigate truncation schemes within the Coupled-
Cluster method\, we have utilized the Kowalski-Piecuch homotopy. In this s
etting\, we have derived an energy error bound for approximate eigenstates
of the Schrödinger equation\, i.e.\, for both ground and excited states.
\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Olivier (University of California\, Berkeley)
DTSTART:20220303T001000Z
DTEND:20220303T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/53
DESCRIPTION:Title: High Order Finite Element Discretizations of the Variable
Eddington Factor Equations for Accelerating Radiation Transport Calculatio
ns on Curved Meshes\nby Samuel Olivier (University of California\, Ber
keley) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nThe
Variable Eddington Factor (VEF) method is one of the oldest techniques for
solving the radiation transport equation. In VEF\, the kinetic equation i
s iteratively coupled to the moment equations through discrete closures. T
his moment-based approach enables significant algorithmic flexibility and
more efficient multiphysics coupling. However\, despite considerable atten
tion in the literature\, VEF is rarely used in practice due to the lack of
scalable iterative preconditioners for the discretized moment equations.
In this talk\, I present three classes of VEF methods with high-order accu
racy on curved meshes that can be efficiently and scalably solved. Discret
ization and preconditioning techniques known to be effective on simpler mo
del elliptic problems are extended to the VEF moment equations to derive D
iscontinuous Galerkin\, continuous finite element\, and mixed finite eleme
nt VEF methods. These methods are demonstrated to be effective on a proxy
problem from thermal radiative transfer in both outer transport iterations
and inner preconditioned linear solver iterations and to scale out to 115
2 processors and over 10 million scalar flux unknowns.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael I Weinstein (Columbia University)
DTSTART:20220406T231000Z
DTEND:20220407T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/54
DESCRIPTION:Title: Discrete honeycombs\, rational edges and edge states\n
by Michael I Weinstein (Columbia University) as part of Berkeley applied m
athematics seminar\n\n\nAbstract\nWe first discuss the derivation of tight
binding (discrete) Hamiltonians from an underlying continuum Schroedinger
Hamiltonians in both non-magnetic and strongly magnetic systems (joint wo
rks with with CL Fefferman and J Shapiro).\n\nWe then present very recent
work (with CL Fefferman and S Fliss) on the tight binding model of graphen
e\, sharply terminated along a rational edge\, a line I parallel to a dire
ction of translational symmetry of the underlying period lattice. We class
ify such edges into those of "zigzag type" and those of "armchair type"\,
generalizing the classical zigzag and armchair edges. Edge states are eige
nstates which are plane wave like in directions parallel to the edge and
are localized in directions transverse to the edge. We prove that zero ene
rgy/flat band edge states arise for edges of zigzag type\, but never for t
hose of armchair type. We exhibit explicit formulas for flat band edge sta
tes when they exist. Finally\, we produce strong evidence for the existenc
e of dispersive (non flat) edge state curves of nonzero energy for most ra
tional edges.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Houman Owhadi (California Institute of Technology)
DTSTART:20220427T231000Z
DTEND:20220428T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/55
DESCRIPTION:Title: Computational Graph Completion\nby Houman Owhadi (Cali
fornia Institute of Technology) as part of Berkeley applied mathematics se
minar\n\n\nAbstract\nWe present a framework for generating\, organizing\,
and reasoning with computational knowledge. It is motivated by the observa
tion that most problems in Computational Sciences and Engineering (CSE) ca
n be formulated as that of completing (from data) a computational graph (o
r hypergraph) representing dependencies between functions and variables. N
odes represent variables\, and edges represent functions. Functions and va
riables may be known\, unknown\, or random. Data comes in the form of obse
rvations of distinct values of a finite number of subsets of the variables
of the graph (satisfying its functional dependencies). The underlying pro
blem combines a regression problem (approximating unknown functions) with
a matrix completion problem (recovering unobserved variables in the data)
. Replacing unknown functions by Gaussian Processes (GPs) and conditionin
g on observed data provides a simple but efficient approach to completing
such graphs. Since this completion process can be reduced to an algorithm\
, as one solves $\\sqrt{2}$ on a pocket calculator without thinking about
it\, one could\, with the automation of the proposed framework\, solve a c
omplex CSE problem by drawing a diagram.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingwei Hu (University of Washington)
DTSTART:20220217T001000Z
DTEND:20220217T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/56
DESCRIPTION:Title: An efficient dynamical low-rank algorithm for the Boltzman
n-BGK equation close to the compressible viscous flow regime\nby Jingw
ei Hu (University of Washington) as part of Berkeley applied mathematics s
eminar\n\n\nAbstract\nIt has recently been demonstrated that dynamical low
-rank algorithms can provide robust and efficient approximations to a rang
e of kinetic equations. This is true especially if the solution is close t
o some asymptotic limit where it is known that the solution is low-rank. A
particularly interesting case is the fluid dynamic limit that is commonly
obtained in the limit of small Knudsen number. However\, in this case the
Maxwellian which describes the corresponding equilibrium distribution is
not necessarily low-rank\; because of this\, the methods known in the lite
rature are only applicable to the weakly compressible case. In this paper\
, we propose an efficient dynamical low-rank integrator that can capture t
he fluid limit—the Navier–Stokes equations—of the Boltzmann-BGK mode
l even in the compressible regime. This is accomplished by writing the sol
ution as f = Mg\, where M is the Maxwellian and the low-rank approximation
is only applied to g. To efficiently implement this decomposition within
a low-rank framework requires\, in the isothermal case\, that certain coef
ficients are evaluated using convolutions\, for which fast algorithms are
known. Using the proposed decomposition also has the advantage that the ra
nk required to obtain accurate results is significantly reduced compared t
o the previous state of the art. We demonstrate this by performing a numbe
r of numerical experiments and also show that our method is able to captur
e sharp gradients/shock waves. This is joint work with Lukas Einkemmer (In
nsbruck) and Lexing Ying (Stanford).\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillaume Bal (University of Chicago)
DTSTART:20220330T231000Z
DTEND:20220331T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/57
DESCRIPTION:Title: Asymmetric transport and topological invariants\nby Gu
illaume Bal (University of Chicago) as part of Berkeley applied mathematic
s seminar\n\n\nAbstract\nRobust asymmetric transport at the interface betw
een two-dimensional insulating bulks has been observed in many areas of (g
eo)physical and materials sciences. The main practical appeal of this asym
metry is its immunity to large classes of perturbations. This stability is
explained by topological considerations.\n \nA physical observable\, a on
e-dimensional conductivity\, is assigned to the asymmetric transport. Inte
rface Hamiltonians modeling the transition between the bulk phases are nex
t introduced and classified by a topological charge\, the index of an appr
opriate Fredholm operator. A general principle\, the bulk-edge corresponde
nce\, then states that the conductivity is quantized and equal to the topo
logical charge\, which may be interpreted as a difference of bulk topologi
es.\n \nWhile ubiquitous in the physical and engineering literatures\, the
bulk-edge correspondence remains difficult to establish mathematically or
in fact even heuristically. This talk presents recent results on the deri
vation of the correspondence for reasonably large algebras of (pseudo-)dif
ferential operators that appear generically as low-energy large-wavelength
models in the applications. We use the correspondence to compute the asym
metry in several settings where a direct estimation seems hopeless\, with
applications\, e.g.\, in graphene-based Floquet topological insulators and
topological properties of twisted bilayer graphene.\n \nTime permitting\,
we will contrast the above spectral properties with the practically more
relevant temporal picture and\, for instance\, the propagation of semi-cla
ssical wavepackets along curved interfaces.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eitan Tadmor (University of Maryland)
DTSTART:20220316T231000Z
DTEND:20220317T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/58
DESCRIPTION:Title: Hierarchical decomposition of images and the problem of Bo
urgain-Brezis\nby Eitan Tadmor (University of Maryland) as part of Ber
keley applied mathematics seminar\n\n\nAbstract\nEdges are noticeable feat
ures in images which can be extracted from noisy data using different vari
ational models. The analysis of such models leads to the question of expre
ssing general L^2-data\, f\, as the divergence of uniformly bounded vector
fields\, div(U). We present a multi-scale approach to construct uniformly
bounded solutions of div(U)=f for general f’s in the critical regularit
y space L^d(T^d). The study of this equation and related problems was moti
vated by results of Bourgain & Brezis. The intriguing critical aspect here
is that although the problems are linear\, construction of their solution
is not. Our constructive solution for such problems is a special case of
a rather general framework for solving linear equations\, formulated as in
verse problems in critical regularity spaces. The solutions are realized i
n terms of nonlinear hierarchical decomposition\, U=image001.png\, which w
e introduced earlier in the context of image processing\, and yield a mult
i-scale decomposition of “objects” U.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dejan Slepcev (Carnegie Mellon University)
DTSTART:20220413T231000Z
DTEND:20220414T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/59
DESCRIPTION:Title: Proper regularizers for semi-supervised learning\nby D
ejan Slepcev (Carnegie Mellon University) as part of Berkeley applied math
ematics seminar\n\n\nAbstract\nWe will discuss a standard problem of semi-
supersised learning: given a data set (considered as a point cloud in a eu
clidean space) with a small number of labeled points the task is to extrap
olate the label values to the whole data set. In order to utilize the geom
etry of the dataset one creates a graph by connecting the nodes which are
sufficiently close. Many standard approaches rely on minimizing graph-base
d functionals\, which reward the agreement with the labels and the regular
ity of the estimator. Choosing a good regularization leads to questions ab
out the relations between discrete functionals in random setting and conti
nuum nonlocal and differential functionals. We will discuss how insights a
bout this relation provide ways to properly choose the functionals for se
mi-supervised learning and appropriately set the weights of the graph so t
hat the information is propagated in a desirable way from the labeled poin
ts. Theoretical results\, numerical illustrations and performance on stand
ard test data sets will be provided.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh Tran (MIT)
DTSTART:20220420T231000Z
DTEND:20220421T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/60
DESCRIPTION:Title: The propagation of information in power-law interacting sy
stems\nby Minh Tran (MIT) as part of Berkeley applied mathematics semi
nar\n\n\nAbstract\nMost physical many-body quantum systems are geometrical
ly local\; it takes time to propagate quantum information in the systems.
Such locality imposes fundamental limits on many quantum information proce
ssing tasks. In this talk\, we will review the state-of-the-art speed limi
ts for the propagation of information in quantum systems with power-law in
teractions. We discuss applications of the speed limits and\, in particula
r\, use them to constrain the propagation of error and improve the perform
ance of quantum simulation algorithms. Inversely\, we also prove new speed
limits using quantum simulation algorithms\, suggesting a deep connection
between the propagation of information and digital quantum simulation.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spring break. No seminar
DTSTART:20220323T231000Z
DTEND:20220324T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/61
DESCRIPTION:by Spring break. No seminar as part of Berkeley applied mathem
atics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Franco (University of California\, Berkeley)
DTSTART:20220310T001000Z
DTEND:20220310T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/62
DESCRIPTION:Title: Relating high-order fluid flow problems to simpler subprob
lems to create efficient preconditioners\nby Michael Franco (Universit
y of California\, Berkeley) as part of Berkeley applied mathematics semina
r\n\n\nAbstract\nThis talk will focus on two solvers for high-order method
s\, with the common thread being that their efficiency derives from relati
ng the original problem to a simpler subproblem. First\, a matrix-free flo
w solver for high-order finite element discretizations of the incompressib
le Navier-Stokes and Stokes equations with GPU acceleration will be presen
ted. For high polynomial degrees\, assembling the matrix for the linear sy
stems resulting from the finite element discretization can be prohibitivel
y expensive\, both in terms of computational complexity and memory. For th
is reason\, it is necessary to develop matrix-free operators and precondit
ioners\, which can be used to efficiently solve these linear systems witho
ut access to the matrix entries themselves. Particular attention will be g
iven to the matrix-free operator evaluations that utilize GPU-accelerated
sum-factorization techniques to minimize memory movement and maximize thro
ughput. I will also briefly introduce novel preconditioners based on a low
-order refined methodology with parallel subspace corrections. Second\, I
will introduce a novel class of iterative subregion correction preconditio
ners for solving flow problems with geometrically localized stiffness. Jus
t as multigrid methods spend more effort on cheaper grids to apply a corre
ction that improves convergence on lower frequency components\, our subreg
ion correction preconditioners spend more effort on a subregion of the dom
ain demonstrating slow convergence to improve overall convergence rates. C
onvergence theory and numerical results validating this theory will be pre
sented.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Di Fang (University of California\, Berkeley)
DTSTART:20220225T001000Z
DTEND:20220225T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/63
DESCRIPTION:Title: Mathematics Department Colloquium: Quantum algorithms for
Hamiltonian simulation with unbounded operators\nby Di Fang (Universit
y of California\, Berkeley) as part of Berkeley applied mathematics semina
r\n\nLecture held in 60 Evans Hall.\n\nAbstract\nRecent years have witness
ed tremendous progress in developing and analyzing quantum algorithms for
quantum dynamics simulation of bounded operators (Hamiltonian simulation).
However\, many scientific and engineering problems require the efficient
treatment of unbounded operators\, which frequently arise due to the discr
etization of differential operators. Such applications include molecular d
ynamics\, electronic structure theory\, quantum control and quantum differ
ential equations solver. We will introduce some recent advances in quantum
algorithms for efficient unbounded Hamiltonian simulation\, including Tro
tter-type splitting and the quantum highly oscillatory protocol (qHOP) in
the interaction picture. The latter yields a surprising superconvergence r
esult for regular potentials.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mo Zhou (Duke University)
DTSTART:20220907T231000Z
DTEND:20220908T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/64
DESCRIPTION:Title: Neural network approaches for high dimensional problems\nby Mo Zhou (Duke University) as part of Berkeley applied mathematics se
minar\n\n\nAbstract\nNeural networks are effective tools for solving high
dimensional problems. In this talk\, I will summarize the popular methods
to solve high dimensional problems with neural networks. Then I will brief
ly introduce two of my works based on the DeepBSDE method. In the first wo
rk\, we solve the eigenvalue problem by transforming it into a fixed-point
formulation\, which is a diffusion Monte Carlo like approach. In the seco
nd work\, we leverage the actor-critic framework from reinforcement learni
ng to solve the static Hamilton—Jacobi—Bellman equations. We propose a
variance reduced temporal difference method for the critic and apply an a
daptive step size algorithm for the actor to improve accuracy.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Wang (University of Minnesota)
DTSTART:20220921T231000Z
DTEND:20220922T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/65
DESCRIPTION:Title: Variational methods for gradient flow\nby Li Wang (Uni
versity of Minnesota) as part of Berkeley applied mathematics seminar\n\n\
nAbstract\nIn this talk\, I will introduce a general variational framework
for nonlinear evolution equations with a gradient flow structure\, which
arise in material science\, animal swarms\, chemotaxis\, and deep learning
\, among many others. Building upon this framework\, we develop numerical
methods that have built-in properties such as positivity preserving and en
tropy decreasing\, and resolve stability issues due to the strong nonlinea
rity. Two specific applications will be discussed. One is the Wasserstein
gradient flow\, where the major challenge is to compute the Wasserstein di
stance and resulting optimization problem. I will show techniques to overc
ome these difficulties. The other is to simulate crystal surface evolution
\, which suffers from significant stiffness and therefore prevents simulat
ion with traditional methods on fine spatial grids. On the contrary\, our
method resolves this issue and is proved to converge at a rate independent
of the grid size.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Leditzky (UIUC)
DTSTART:20220928T231000Z
DTEND:20220929T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/66
DESCRIPTION:Title: The platypus of the quantum channel zoo\nby Felix Ledi
tzky (UIUC) as part of Berkeley applied mathematics seminar\n\n\nAbstract\
nUnderstanding quantum channels and the strange behavior of their capaciti
es is a key driver of quantum information theory. Despite having rigorous
coding theorems\, quantum capacities are poorly understood due to super-ad
ditivity effects. We will talk about a remarkably simple\, low-dimensional
\, single-parameter family of quantum channels with exotic quantum informa
tion-theoretic features. As the simplest example from this family\, we foc
us on a qutrit-to-qutrit channel that is intuitively obtained by hybridizi
ng together a simple degradable channel and a completely useless qubit cha
nnel. Such hybridizing makes this channel's capacities behave in a variety
of interesting ways. For instance\, the private and classical capacity of
this channel coincide and can be explicitly calculated\, even though the
channel does not belong to any class for which the underlying information
quantities are known to be additive. Moreover\, the quantum capacity of th
e channel can be computed explicitly\, given a clear and compelling conjec
ture is true. This "spin alignment conjecture\," which may be of independe
nt interest\, is proved in certain special cases and additional numerical
evidence for its validity is provided. We further show that this qutrit ch
annel demonstrates superadditivity when transmitting quantum information j
ointly with a variety of assisting channels\, in a manner unknown before.
A higher-dimensional variant of this qutrit channel displays super-additiv
ity of quantum capacity together with an erasure channel. Subject to the s
pin-alignment conjecture\, our results on super-additivity of quantum capa
city extend to lower-dimensional channels as well as larger parameter rang
es. In particular\, super-additivity occurs between two weakly additive ch
annels each with large capacity on their own\, in stark contrast to previo
us results. Remarkably\, a single\, novel transmission strategy achieves s
uper-additivity in all examples. Our results show that super-additivity is
much more prevalent than previously thought. It can occur across a wide v
ariety of channels\, even when both participating channels have large quan
tum capacity.\n\nThis is joint work with Debbie Leung\, Vikesh Siddhu\, Gr
aeme Smith\, and John Smolin\, and based on the papers https://arxiv.org/a
bs/2202.08380 and https://arxiv.org/abs/2202.08377.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Ma (Stanford University)
DTSTART:20221005T231000Z
DTEND:20221006T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/67
DESCRIPTION:Title: Implicit bias of optimization algorithms for neural networ
ks and their effects on generalization\nby Chao Ma (Stanford Universit
y) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nModern n
eural networks are usually over-parameterized—the number of parameters e
xceeds the number of training data. In this case the loss functions tend t
o have many (or even infinite) global minima\, which imposes an additional
challenge of minima selection on optimization algorithms besides the conv
ergence. Specifically\, when training a neural network\, the algorithm not
only has to find a global minimum\, but also needs to select minima with
good generalization among many other bad ones. In this talk\, I will share
a series of works studying the mechanisms that facilitate global minima s
election of optimization algorithms. First\, with a linear stability theor
y\, we show that stochastic gradient descent (SGD) favors flat and uniform
global minima. Then\, we build a theoretical connection of flatness and g
eneralization performance based on a special structure of neural networks.
Next\, we study the global minima selection dynamics—the process that a
n optimizer leaves bad minima for good ones—in two settings. For a manif
old of minima around which the loss function grows quadratically\, we deri
ve effective exploration dynamics on the manifold for SGD and Adam\, using
a quasistatic approach. For a manifold of minima around which the loss fu
nction grows subquadratically\, we study the behavior and effective dynami
cs for GD\, which also explains the edge of stability phenomenon.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Fornace (Caltech)
DTSTART:20221012T231000Z
DTEND:20221013T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/68
DESCRIPTION:Title: Theoretical methods for nucleic acid secondary structure t
hermodynamics and kinetics\nby Mark Fornace (Caltech) as part of Berke
ley applied mathematics seminar\n\n\nAbstract\nNucleic acid secondary stru
cture models offer a simplified but powerful lens through which to view\,
analyze\, and design nucleic acid chemistry. Computational approaches base
d on such models are central to current research directions across molecul
ar programming and the life sciences more broadly. Considering only struct
ures involving noncrossing partitions of nucleotides\, dynamic programming
algorithms can exactly compute equilibrium quantities (with respect to an
approximate free energy model) in cubic complexity. I first show how such
algorithms may be improved in speed\, augmented in accuracy\, and unified
across a variety of physical quantities.\n\nWhile analysis and design par
adigms for nucleic acid thermodynamics are long-established in essence\, n
ucleic acid kinetics have proved vexing for accurate and principled estima
tion algorithms. Past approaches have thus generally relied on stochastic
simulation of the respective continuous time Markov chains (an asymptotica
lly correct but computationally costly approach). In contrast\, I show how
a principled Galerkin-type approach to the kinetics proves remarkably ame
nable to deterministic estimation by dynamic programming algorithms. While
inexact\, the approach proves empirically accurate and is theoretically e
xtensible to treatments of mass-action kinetics\, macrostate models\, and
sequence design.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Gao (University of Houston)
DTSTART:20221019T231000Z
DTEND:20221020T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/69
DESCRIPTION:Title: Logarithmic Sobolev inequalities for matrices and matrix-v
alued functions\nby Li Gao (University of Houston) as part of Berkeley
applied mathematics seminar\n\n\nAbstract\nLogarithmic Sobolev inequaliti
es\, first introduced by Gross in 70s\, have rich connections to probabili
ty\, geometry\, as well as information theory. In recent years\, logarithm
ic Sobolev inequalities for quantum Markov semigroups attracted a lot of a
ttentions for its applications in quantum information theory and quantum m
any-body systems. In this talk\, I'll present a simple\, information-theor
etic approach to modified logarithmic Sobolev inequalities for both quantu
m Markov semigroup on matrices\, and classical Markov semigroup on matrix-
valued functions. In the classical setting\, our results implies every sub
-Laplacian of a Hörmander system admits a uniform modified logarithmic S
obolev constant for all its matrix valued functions. For quantum Markov se
migroups\, we improve a previous result of Gao and Rouzé by replacing the
dimension constant by its logarithm. This talk is based on a joint work w
ith Marius Junge\, Nicholas\, LaRacunte\, and Haojian Li.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Colbrook (University of Cambridge)
DTSTART:20221024T231000Z
DTEND:20221025T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/70
DESCRIPTION:Title: Residual Dynamic Mode Decomposition: Rigorous Data-Driven
Computation of Spectral Properties of Koopman Operators for Dynamical Syst
ems\nby Matthew Colbrook (University of Cambridge) as part of Berkeley
applied mathematics seminar\n\n\nAbstract\nKoopman operators are infinite
-dimensional operators that globally linearize\nnonlinear dynamical system
s\, making their spectral information valuable for\nunderstanding dynamics
. However\, Koopman operators can have continuous\nspectra\, can lack fini
te-dimensional invariant subspaces\, and approximations can\nsuffer from s
pectral pollution (spurious modes). These issues make computing\nthe spect
ral properties of Koopman operators a considerable challenge. This two-\np
art talk will detail the first scheme (ResDMD) with convergence guarantees
for\ncomputing the spectra and pseudospectra of general Koopman operators
from\nsnapshot data. Furthermore\, we use the resolvent operator and ResD
MD to\ncompute smoothed approximations of spectral measures (including con
tinuous\nspectra)\, with explicit high-order convergence. ResDMD is simila
r to extended\nDMD\, except it rigorously concurrently computes a residual
from the same\nsnapshot data\, allowing practitioners to gain confidence
in the computed results.\nKernelized variants of our algorithms allow for
dynamical systems with a high-\ndimensional state-space\, and the error co
ntrol provided by ResDMD allows a\nposteriori verification of learnt dicti
onaries. We apply ResDMD to compute the\nspectral measure associated with
the dynamics of a protein molecule (20\,046-dimensional state-space) and d
emonstrate several problems in fluid dynamics\n(with state-space dimension
s > 100\,000). For example\, we compare ResDMD\nand DMD for particle image
velocimetry data from turbulent wall-jet flow\, the\nacoustic signature o
f laser-induced plasma\, and turbulent flow past a cascade of\naerofoils.\
n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Lanthaler (Caltech)
DTSTART:20221110T001000Z
DTEND:20221110T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/71
DESCRIPTION:Title: Supervised learning in function space\nby Samuel Lanth
aler (Caltech) as part of Berkeley applied mathematics seminar\n\n\nAbstra
ct\nNeural networks have proven to be effective approximators of high dime
nsional functions in a wide variety of applications. In scientific applica
tions the goal is often to approximate an underlying operator\, which defi
nes a mapping between infinite-dimensional spaces of input and output func
tions. Extensions of neural networks to this infinite-dimensional setting
have been proposed in recent years\, giving rise to the rapidly emerging f
ield of operator learning. Despite their practical success\, our theoretic
al understanding of these approaches is still in its infancy. In this talk
\, I will review some of the proposed operator learning architectures (dee
p operator networks/neural operators)\, and present recent results on thei
r approximation theory and sample complexity. This work identifies basic m
echanisms by which neural operators can avoid a curse of dimensionality in
the underlying (very high- or even infinite-dimensional) approximation ta
sk\, thus providing a first rationale for their practical success for conc
rete operators of interest. The analysis also reveals fundamental limitati
ons of some of these approaches.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Bouck (University of Maryland)
DTSTART:20221117T001000Z
DTEND:20221117T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/72
DESCRIPTION:Title: Finite Element Approximation of a Membrane Model for Liqui
d Crystal Polymeric Networks\nby Lucas Bouck (University of Maryland)
as part of Berkeley applied mathematics seminar\n\n\nAbstract\nLiquid crys
tal polymeric networks are materials where a nematic liquid crystal is cou
pled with a rubbery material. When actuated with heat or light\, the inter
action of the liquid crystal with the rubber creates complex shapes. Start
ing from the classical 3D trace formula energy of Bladon\, Warner and Tere
ntjev (1994)\, we derive a 2D membrane energy as the formal asymptotic lim
it of the 3D energy. The derivation is similar to derivations in Ozenda\,
Sonnet\, and Virga (2020) and Cirak et. al. (2014). We characterize the ze
ro energy deformations and prove that the energy lacks certain convexity p
roperties. We propose a finite element method to discretize the problem. T
o address the lack of convexity of the membrane energy\, we regularize wit
h a term that mimics a higher order bending energy. We prove that minimize
rs of the discrete energy converge to minimizers of the continuous energy.
For minimizing the discrete problem\, we employ a nonlinear gradient flow
scheme\, which is energy stable. Additionally\, we present computations s
howing the geometric effects that arise from liquid crystal defects. Compu
tations of configurations from nonisometric origami are also presented.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No seminar. Happy thanksgiving.
DTSTART:20221124T001000Z
DTEND:20221124T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/73
DESCRIPTION:by No seminar. Happy thanksgiving. as part of Berkeley applied
mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sui Tang (UCSB)
DTSTART:20221201T001000Z
DTEND:20221201T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/74
DESCRIPTION:Title: Bridging the interacting particle models and data science
via Gaussian process\nby Sui Tang (UCSB) as part of Berkeley applied m
athematics seminar\n\n\nAbstract\nSystem of interacting particles that dis
play a wide variety of collective behaviors are ubiquitous in science and
engineering\, such as self-propelled particles\, flocking of birds\, milli
ng of fish. Modeling interacting particle systems by a system of different
ial equations plays an essential role in exploring how individual behavior
engenders collective behaviors\, which is one of the most fundamental and
important problems in various disciplines. Although the recent theoretic
al and numerical study bring a flood of models that can reproduce many mac
roscopical qualitative collective patterns of the observed dynamics\, the
quantitative study towards matching the well-developed models to observat
ional data is scarce. \n\nWe consider the data-driven discovery of macrosc
opic particle models with latent interactions. We propose a learning appro
ach that models the latent interactions as Gaussian processes\, which prov
ides an uncertainty-aware modeling of interacting particle systems. We int
roduce an operator-theoretic framework to provide a detailed analysis of r
ecoverability conditions\, and establish statistical optimality of the pro
posed approach. Numerical results on prototype systems and real data demo
nstrate the effectiveness of the proposed approach.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krutika Tawri (University of California\, Berkeley)
DTSTART:20220914T231000Z
DTEND:20220915T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/75
DESCRIPTION:Title: On stochastic partial differential equations with a Ladyze
nskaya-Smagorinsky type nonlinearity\nby Krutika Tawri (University of
California\, Berkeley) as part of Berkeley applied mathematics seminar\n\n
Lecture held in 939 Evans Hall.\n\nAbstract\nThe theory of monotone operat
ors plays a central role in many areas of nonlinear analysis. Monotone ope
rators often appear in fluid dynamics\, for example the p-Laplacian appear
s in a non-Newtonian variant of the Navier-Stokes equations modeled by Lad
yzenskaya or in the Smagorinsky model of turbulence. In this talk\, we wil
l discuss global existence results of both martingale and pathwise solutio
ns of stochastic equations with a monotone operator\, of the Ladyzenskaya-
Smagorinsky type\, driven by a general Levy noise. The classical approach
based on using directly the Galerkin approximation is not valid. In this t
alk we will discuss how one can approximate a monotone operator by a famil
y of monotone operators acting in a Hilbert space\, so as to recover certa
in useful properties of the orthogonal projectors and overcome the challen
ges faced while applying the Galerkin scheme.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yonah Borns-Weil (University of California\, Berkeley)
DTSTART:20221102T231000Z
DTEND:20221103T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/76
DESCRIPTION:Title: Observable Trotter error bounds in the semiclassical regim
e\nby Yonah Borns-Weil (University of California\, Berkeley) as part o
f Berkeley applied mathematics seminar\n\n\nAbstract\nThe Trotter product
formula is perhaps the oldest and most well-known method for computing Sch
rödinger propagators. We consider its application to the semiclassical Sc
hrodinger equation where the parameter $h$ is taken to be very small. If o
ne wishes to do practical computations in such a regime\, they must take a
t least $O(h^{-1})$ spatial grid points\, which gives the Hamiltonian term
s and their nested commutators to be of norm O(h^{-1}). This would appear
to cause serious trouble for both Trotter and post-Trotter methods\, as th
eir time complexity depends on such norms.\n\nThe issue resolves itself wh
en we consider approximating the propagator in observable norm\, which mea
sures how much an observable propagated via the actual Hamiltonian differs
from one propagated by our Trotter approximation. By a simple argument us
ing Egorov's theorem from semiclasscial analysis\, we show the error in th
is norm to be uniform in the semiclassical parameter $h$. In addition\, we
consider the discretized space case of interest in quantum computing\, an
d use discrete microlocal analysis on the quantized torus to extend our re
sults to this case without added error.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Govind Menon (Brown University)
DTSTART:20230121T001000Z
DTEND:20230121T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/77
DESCRIPTION:Title: Stochastic Nash evolution\nby Govind Menon (Brown Univ
ersity) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nAbo
ut ten years ago\, De Lellis and Szekelyhidi made the surprising discovery
that Nash’s results on the isometric embedding problem for Riemannian m
anifoldscould be adapted to construct counterintuitive solutions to the Eu
ler equations for incompressible flow. Their work shed new light on turbul
ence and nonlinear PDE. We use this link in the other direction\, transfer
ring ideas from turbulence to geometry.\n\nA thermodynamic framework is in
troduced that connects two problems previously thought to be distinct: the
isometric embedding problem for Riemannian manifolds and the construction
of Brownian motion on Riemannian manifolds. This link is used to introduc
e a geometric stochastic flow that we term stochastic Nash evolution.\n\nT
hese ideas will be explained in a (hopefully) elementary manner. My main g
oal is to present the stochastic flows in a manner that is suited to imple
mentations by modifications of level set methods. The absence of numerical
computations of isometric embeddings is an important gap in our understan
ding.\n\nThis is joint work with Dominik Inauen (University of Leipzig).\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anuj Kumar (UC Santa Cruz)
DTSTART:20230126T001000Z
DTEND:20230126T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/78
DESCRIPTION:Title: Application of branching flows to optimal scalar transport
and a result concerning the nonuniqueness of trajectories\nby Anuj Ku
mar (UC Santa Cruz) as part of Berkeley applied mathematics seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Albergo (New York University)
DTSTART:20230223T001000Z
DTEND:20230223T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/79
DESCRIPTION:by Michael Albergo (New York University) as part of Berkeley a
pplied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiantao Li (Penn State University)
DTSTART:20230302T001000Z
DTEND:20230302T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/80
DESCRIPTION:Title: Efficient algorithms for quantum optimal control problems<
/a>\nby Xiantao Li (Penn State University) as part of Berkeley applied mat
hematics seminar\n\n\nAbstract\nMany recent developments in chemistry and
material science utilize systems that exhibit unique quantum properties. A
quantum optimal control strategy can maximize the performance of electron
ic devices that rely on quantum properties\, e.g.\, minimizing the current
s in molecular junctions. Computationally\, solving the control problem re
quires visiting the time-dependent Schrödinger equation frequently\, and
the corresponding solutions will be combined with an optimization method.
In this talk\, we examine the overall approximation error and estimate the
complexity given the error tolerance. We focus on various methods for int
egrating optimization algorithms and Hamiltonian simulations to achieve pr
ovable accuracy.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fanhui Xu (Harvard University)
DTSTART:20230315T231000Z
DTEND:20230316T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/81
DESCRIPTION:by Fanhui Xu (Harvard University) as part of Berkeley applied
mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Fang Chen (Caltech)
DTSTART:20230322T231000Z
DTEND:20230323T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/82
DESCRIPTION:Title: Sparse random Hamiltonians are quantumly easy\nby Chi-
Fang Chen (Caltech) as part of Berkeley applied mathematics seminar\n\n\nA
bstract\nA candidate application for quantum computers is to simulate the
low-temperature properties of quantum systems. For this task\, there is a
well-studied quantum algorithm that performs quantum phase estimation on a
n initial trial state that has a nonnegligible overlap with a low-energy s
tate. However\, it is notoriously hard to give theoretical guarantees that
such a trial state can be prepared efficiently. Moreover\, the heuristic
proposals that are currently available\, such as with adiabatic state prep
aration\, appear insufficient in practical cases. This paper shows that\,
for most random sparse Hamiltonians\, the maximally mixed state is a suffi
ciently good trial state\, and phase estimation efficiently prepares state
s with energy arbitrarily close to the ground energy. Furthermore\, any lo
w-energy state must have nonnegligible quantum circuit complexity\, sugges
ting that low-energy states are classically nontrivial and phase estimatio
n is the optimal method for preparing such states (up to polynomial factor
s). These statements hold for two models of random Hamiltonians: (i) a sum
of random signed Pauli strings and (ii) a random signed d-sparse Hamilton
ian. The main technical argument is based on some new results in nonasympt
otic random matrix theory. In particular\, a refined concentration bound f
or the spectral density is required to obtain complexity guarantees for th
ese random Hamiltonians.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar. spring break
DTSTART:20230329T231000Z
DTEND:20230330T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/83
DESCRIPTION:by no seminar. spring break as part of Berkeley applied mathem
atics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangwen Zhang (Carnegie Mellon University)
DTSTART:20230405T231000Z
DTEND:20230406T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/84
DESCRIPTION:by Yangwen Zhang (Carnegie Mellon University) as part of Berke
ley applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandeep Sharma (University of Colorado Boulder)
DTSTART:20230412T231000Z
DTEND:20230413T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/85
DESCRIPTION:by Sandeep Sharma (University of Colorado Boulder) as part of
Berkeley applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uros Seljak (UC Berkeley)
DTSTART:20230419T231000Z
DTEND:20230420T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/86
DESCRIPTION:by Uros Seljak (UC Berkeley) as part of Berkeley applied mathe
matics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandar Donev (Courant Institute)
DTSTART:20230317T231000Z
DTEND:20230318T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/87
DESCRIPTION:Title: Hydrodynamics and rheology of fluctuating\, semiflexible\,
inextensible\, and slender filaments in Stokes flow\nby Aleksandar Do
nev (Courant Institute) as part of Berkeley applied mathematics seminar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyan Ding (UC Berkeley)
DTSTART:20230209T001000Z
DTEND:20230209T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/88
DESCRIPTION:Title: Mean-field analysis of interacting particle system and ove
rparameterization of neural network\nby Zhiyan Ding (UC Berkeley) as p
art of Berkeley applied mathematics seminar\n\n\nAbstract\nThe interacting
particle system is a dynamic system that contains a lot of interacting pa
rticles. Because of the interaction between different particles\, the dire
ct analysis and simulation of the system are very difficult. The mean-fiel
d analysis is a framework for analyzing these large interacting particle s
ystems. In this framework\, instead of directly studying the coupled syste
m\, one approximates the system by a partial differential equation whose s
olution characterizes the distribution of the particles. This strategy lar
gely simplifies the problem and provides a more efficient way to study the
evolution of the particle system. In this talk\, I will mainly focus on t
he derivation of the mean-field analysis and its application in analyzing
overparameterization of neural network.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uros Seljak (UC Berkeley)
DTSTART:20230216T001000Z
DTEND:20230216T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/89
DESCRIPTION:by Uros Seljak (UC Berkeley) as part of Berkeley applied mathe
matics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Urban (MIT)
DTSTART:20230309T001000Z
DTEND:20230309T010000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/90
DESCRIPTION:by Julian Urban (MIT) as part of Berkeley applied mathematics
seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuehaw Khoo (University of Chicago)
DTSTART:20230426T231000Z
DTEND:20230427T000000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/91
DESCRIPTION:by Yuehaw Khoo (University of Chicago) as part of Berkeley app
lied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eun-Jae Park (Yonsei University)
DTSTART:20230615T173000Z
DTEND:20230615T183000Z
DTSTAMP:20260404T095626Z
UID:BerekelyApplied/92
DESCRIPTION:Title: Polygonal Staggered Galerkin Methods\nby Eun-Jae Park
(Yonsei University) as part of Berkeley applied mathematics seminar\n\n\nA
bstract\nIn this talk\, we first present the staggered discontinuous Galer
kin method on general meshes for the Poisson equation. Adaptive mesh refin
ement is an attractive tool for general meshes due to their flexibility an
d simplicity in handling hanging nodes. We derive a simple residual-type e
rror estimator. Numerical results indicate that optimal convergence can be
achieved for both the potential and vector variables\, and the singularit
y can be well-captured by the proposed error estimator. Then\, some applic
ations to interface problems are considered such as coupling of Darcy-Forc
hheimer and Stokes equations\, and a single-phase flow in porous media wit
h a fracture. In the case of s fractured porous media\, the bulk variables
are solved using staggered DG method and an interface variable is solved
using the continuous Galerkin method. We derive optimal convergence for bo
th pressure and velocity fields. Numerical experiments suggest that our me
thod is more accurate when polygonal meshes are used among various mesh co
nfigurations\; moreover\, our method is robust to mesh distortion. These o
bservations allow us to consider unfitted methods without any special trea
tment. With background meshes generated independent of fracture\, numerica
l solutions converge in optimal order.\n\nThis is joint work with Eric Chu
ng\, Dohyun Kim\, and Lina Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/BerekelyApplied/92/
END:VEVENT
END:VCALENDAR