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BEGIN:VEVENT
SUMMARY:Sergey Buterin\, Nebojsa Djuric
DTSTART:20220308T140000Z
DTEND:20220308T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/1
DESCRIPTION:Title: Inverse spectral problems for Dirac operators withconstant
delay: uniqueness\, characterization\, uni-form stability\nby Sergey B
uterin\, Nebojsa Djuric as part of Seminars on Inverse Problems Theory and
Applications\n\n\nAbstract\nWe initiate studying inverse spectral problem
s for Dirac-type functional-differential operators with constant delay. Fo
r simplicity\, we restrict ourselves to the case when the delay parameter
is not less than one-half of the interval. For the considered case\, howev
er\, we give answers to the full range of questions usually raised in the
inverse spectral theory. Specifically\, reconstruction of two complex $L_2
$-potentials is studied from either complete spectra or subspectra of two
boundary value problems with one common boundary condition. We give condit
ions on the subspectra that are necessary and sufficient for the unique de
termination of the potentials. Moreover\, necessary and sufficient conditi
ons for the solvability of both inverse problems are obtained. For the inv
erse problem involving the complete spectra\, we establish also uniform st
ability in each ball of a finite radius. For this purpose\, we use recent
results on uniform stability of sine-type functions with asymptotically se
parated zeros.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Per Christian Hansen (Technical University of Denmark)
DTSTART:20220419T140000Z
DTEND:20220419T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/2
DESCRIPTION:Title: IR Tools: Iterative Regularization for Inverse Prob- lems\nby Per Christian Hansen (Technical University of Denmark) as part of S
eminars on Inverse Problems Theory and Applications\n\n\nAbstract\nThe Mat
lab package IR Tools provides implementations of a range of\niterative sol
vers for linear inverse problems\, and a set of large-scale test\nproblems
in the form of discretizations of 2D linear inverse problems.\nWe include
iterative regularization methods where the regularization is\ndue to the
semi-convergence\, and Tikhonov-type formulations where\nthe regularizatio
n is due to a regularization term. In both cases\, we can\nimpose bound co
nstraints on the solution. We implemented the iterative\nmethods in a flex
ible fashion that allows the problem’s coefficient matrix\nto be availab
le as a (sparse) matrix\, a function handle\, or an object. The\nbasic cal
l to all of the iterative methods requires only this matrix and the\nright
-hand side. Our codes automatically set default parameters of the\nstoppin
g rules\, regularization parameters\, etc.\; with an optional input\nstruc
ture\, the user has full control of any of these algorithm parameters.\nTh
e test problems represent realistic large-scale problems found in image\nr
econstruction and several other applications. These new test problems\nrep
lace the small and outdated test problems from 1994 in Regularization\nToo
ls. The basic call to all of the test problem generators produces a\nmatri
x\, a right-hand side and the corresponding exact solution. Similar\nto th
e iterative methods\, the user can use an optional input structure to\ncon
trol specific features of the test problem.\nThis is joint work with Silvi
a Gazzola and James G. Nagy.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Kuznetsova (Saratov State University)
DTSTART:20220503T140000Z
DTEND:20220503T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/3
DESCRIPTION:Title: Inverse problem for the Sturm–Liouville operators with fr
ozen argument\nby Maria Kuznetsova (Saratov State University) as part
of Seminars on Inverse Problems Theory and Applications\n\n\nAbstract\nThe
talk is devoted to recovering the Sturm–Liouville operator with frozen
argument from its spectrum. Unique solvability of this inverse problem dep
ends on the position of frozen argument and the boundary conditions. We co
mpare different approaches to the inverse problem and the corresponding re
sults in two cases of rational and irrational frozen argument. Further\, w
e suggest a new unified approach to operators with frozen argument\, which
is effective in the both cases.\n\nApplying it\, we obtain new-type asymp
totic formulae completely characterizing the class of sequences that can b
e the spectra of the considered operators.\n\nThis talk is based on the pa
per: Kuznetsova\, M. Necessary and sufficient conditions for the spectra o
f the Sturm–Liouville operators with frozen argument\, Applied Mathemati
cs Letters 131 (2022)\, article 108035.\n\nThe paper is available via the
link https://authors.elsevier.com/a/1enGg3BGwfEDzY\n\nMeeting ID: 967 6835
8960\nPasscode: 705810\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Rowlett (Chalmers University of Technology)
DTSTART:20220607T140000Z
DTEND:20220607T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/4
DESCRIPTION:Title: The mathematics of ``hearing the shape of a drum''\nby
Julie Rowlett (Chalmers University of Technology) as part of Seminars on I
nverse Problems Theory and Applications\n\n\nAbstract\nHave you heard the
question "Can one hear the shape of a drum?" Do you know the answer? In 19
66\, M. Kac's article of the same title popularized the inverse isospectra
l problem for planar domains. Twenty-six years later\, Gordon\, Webb\, and
Wolpert demonstrated the answer\, but many naturally related problems rem
ain open today. We will discuss old and new results inspired by "hearing t
he shape of a drum."\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuncay Aktosun (University of Texas at Arlington)
DTSTART:20220920T140000Z
DTEND:20220920T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/5
DESCRIPTION:Title: The Marchenko inversion method for the derivative NLS syste
m\nby Tuncay Aktosun (University of Texas at Arlington) as part of Sem
inars on Inverse Problems Theory and Applications\n\n\nAbstract\nThe March
enko method is presented for the linear system associated with the derivat
ive NLS (nonlinear Schrödinger) system. The system of linear Marchenko in
tegral equations is derived in order to solve the corresponding inverse sc
attering problem. Through the use of the inverse scattering transform\, so
lutions are obtained for the derivative NLS system. Explicit solution form
ulas are developed in closed form by using as input a pair of matrix tripl
ets corresponding to reflectionless scattering data.\n\n*The meeting id an
d passcode will be emailed to the seminar mailing list.\n\n** For more inf
ormation please visit our webpage: https://www.inverseproblemseminars.com\
n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Pallikarakis (National Technical University of Athens)
DTSTART:20221004T140000Z
DTEND:20221004T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/6
DESCRIPTION:Title: Inverse Spectral Problems for Classic and Modified Transmis
sion Eigenvalues\nby Nikolaos Pallikarakis (National Technical Univers
ity of Athens) as part of Seminars on Inverse Problems Theory and Applicat
ions\n\n\nAbstract\nResearch on transmission eigenvalues has been a very a
ctive topic in inverse scattering theory. In this talk\, we discuss about
the inverse transmission eigenvalue problem for the spherically symmetric
refractive index. We present some well-known uniqueness results for the co
ntinuous case [1]. Next\, we highlight the need to introduce modified prob
lems and demonstrate the corresponding modified transmission eigenvalue pr
oblem [2]. A new uniqueness result for the inverse problem is derived [3].
We conclude by summarizing similarities and differences among inverse pro
blems using classic and modifed transmission eigenvalues.\n\n[1] Gintides
D and Pallikarakis N\, The inverse transmission eigenvalue problem for a d
iscontinuous refractive index\, Inverse Problems\, 33\, 2017.\n\n[2] Ginti
des D\, Pallikarakis N and Stratouras K\, On the modified transmission eig
envalue problem with an artificial metamaterial background\, Res. Math. Sc
i.\, 8\, 2021\, (special issue on transmission eigenvalues).\n\n[3] Gintid
es D\, Pallikarakis N and Stratouras K\, Uniqueness of a spherically symme
tric refractive index from modified transmission eigenvalues\, Inverse Pro
blems\, 38\, 2022.\n\nThe meeting id and passcode will be emailed to the s
eminar mailing list. For more information please visit our webpage: https:
//www.inverseproblemseminars.com\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangfang Liu (Michigan Technical University)
DTSTART:20221018T140000Z
DTEND:20221018T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/7
DESCRIPTION:Title: Deterministic-Statistical Approach for an Inverse Acoustic
Source Problem using Multiple Frequency Limited Aperture Data\nby Yang
fang Liu (Michigan Technical University) as part of Seminars on Inverse Pr
oblems Theory and Applications\n\n\nAbstract\nWe propose a deterministic-s
tatistical method for an inverse source problem using multiple frequency l
imited aperture far field data. The direct sampling method is used to obta
in a disc such that it contains the compact support of the source. The Dir
ichlet eigenfunctions of the disc are used to expand the source function.
Then the inverse problem is recast as a statistical inference problem for
the expansion coefficients and the Bayesian inversion is employed to recon
struct the coefficients. The stability of the statistical inverse problem
with respect to the measured data is justified in the sense of Hellinger d
istance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) al
gorithm is implemented to explore the posterior density function of the un
knowns. Numerical examples show that the proposed method is effective for
both smooth and non-smooth sources given limited-aperture data.\n\nThe mee
ting id and passcode will be emailed to the seminar mailing list. For more
information please visit our webpage: https://www.inverseproblemseminars.
com\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Onur Baysal (University of Malta)
DTSTART:20221101T140000Z
DTEND:20221101T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/8
DESCRIPTION:Title: A New Numerical Approach for Identifiying Source Function i
n a Plate Equation\nby Onur Baysal (University of Malta) as part of Se
minars on Inverse Problems Theory and Applications\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masatoshi Suzuki (Tokio Institute of Technology)
DTSTART:20221115T140000Z
DTEND:20221115T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/9
DESCRIPTION:Title: An inverse problem for a class of canonical systems with no
indivisible intervals\nby Masatoshi Suzuki (Tokio Institute of Techno
logy) as part of Seminars on Inverse Problems Theory and Applications\n\n\
nAbstract\nA Hamiltonian is a 2-by-2 positive semidefinite real symmetric
matrix-valued function defined on an interval whose components are locally
integrable. A canonical system is a first-order system of linear differen
tial equations parametrized by complex numbers associated with a given Ham
iltonian. The solution of a canonical system gives an entire function of t
he Hermite–Biehler class.\n\nIn this talk\, we solve the inverse problem
which recovers a Hamiltonian from a given function E in the Hermite–Bie
hler class under some special assumptions on E.\n\nThe method of the solut
ion is similar to the solution of the inverse problem for strings given\nb
y M. G. Krein but is different. We will also explain the difference.\n\nTh
e meeting id and passcode will be emailed to the seminar mailing list. For
more information please visit our webpage: https://www.inverseproblemsemi
nars.com\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sehrish Javed (Comsats University Islamabad)
DTSTART:20221129T140000Z
DTEND:20221129T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/10
DESCRIPTION:by Sehrish Javed (Comsats University Islamabad) as part of Sem
inars on Inverse Problems Theory and Applications\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. A. Yurko (Saratov State University)
DTSTART:20221206T140000Z
DTEND:20221206T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/11
DESCRIPTION:Title: Inverse problems for discrete operators\nby V. A. Yurk
o (Saratov State University) as part of Seminars on Inverse Problems Theor
y and Applications\n\n\nAbstract\nWe give a short review of results on inv
erse spectral problems for wide classes of discrete operators. We start wi
th the simplest class of Jacobi operators. Then we will pay attention\non
other more complicated classes of discrete operators. We will use a unifie
d approach for studying different classes\nof discrete operators.\n\nThe m
eeting id and passcode will be emailed to the seminar mailing list. For m
ore information please visit our webpage: https://www.inverseproblemsemina
rs.com\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.S. Osipov (Scientific-Research Institute for System Analysis of
the Russian Academy of Sciences)
DTSTART:20230221T140000Z
DTEND:20230221T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/12
DESCRIPTION:Title: Inverse spectral problem and Volterra type lattices\nb
y A.S. Osipov (Scientific-Research Institute for System Analysis of the Ru
ssian Academy of Sciences) as part of Seminars on Inverse Problems Theory
and Applications\n\n\nAbstract\nIn this talk\, we mainly consider some iss
ues related to the study of Volterra lattice (also known as Kac-van Moerbe
ke system\, Langmuir chain or discrete Korteweg-de Vries equation) in the
semi-infinite case. In particular\, we consider its integration via Lax pa
ir formalism by means of the inverse spectral problem for (Jacobi-like) se
cond order difference operators. The key role in this inverse problem inte
gration method is played by the moments of the Weyl function of the corres
ponding difference operator\, which appears in the Lax representation for
this lattice\, and their evolution in time. We discuss the extension of th
is method to another classes of nonlinear dynamical systems (e.g. Bogoyavl
ensky lattices) and their other applications to the theory of nonlinear in
tegrable equations. This talk is partly based on the following papers:\n\n
[1] Osipov A.S. (2020) Inverse spectral problems for second-order differen
ce operators and their application to the study of Volterra type systems\,
Rus. J. Nonlin. Dyn.\, 16:3\, 397--419. (available at http://nd.ics.org.r
u/nd200301/ )\n\n[2] Osipov A.S. (2021) Inverse spectral problem for Jacob
i operators and Miura transformation\, Concr. Oper.\, 8:1\, 77--89.(availa
ble at https://doi.org/10.1515/conop-2020-0116 )\n\n[3] Osipov A. S. (2022
) Inverse spectral problem for band operators and their sparsity criterion
in terms of inverse problems data\, Russian Journal of Mathematical Physi
cs\, 29:2\, 225--237.\n\nThe meeting id and passcode will be emailed to th
e seminar mailing list. For more information please visit our webpage: www
.inverseproblemseminars.com\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karel Van Bockstal (Ghent University)
DTSTART:20230307T140000Z
DTEND:20230307T150000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/13
DESCRIPTION:Title: Inverse source problem in time-fractional diffusion equati
ons with non-smooth solutions\nby Karel Van Bockstal (Ghent University
) as part of Seminars on Inverse Problems Theory and Applications\n\n\nAbs
tract\nThis talk is based on the papers [1] and [2]. In [1]\, an inverse s
ource problem (ISP) for a time-fractional diffusion equation of order $\\a
lpha\\in(0\,1)$ is discussed. The missing solely time-dependent source is
recovered from an additional integral measurement. An additional challenge
is that the coefficients of the elliptic operator considered are dependen
t on spatial and time variables. Two research questions are of concern in
this talk: (i) the existence and uniqueness of a (weak) solution to the IS
P for exact data\, and (ii) the numerical reconstruction of the unknown so
urce. Moreover\, the extension of the results to multiterm time-fractional
diffusion equation [2]\, and directions for future work will be discussed
. \n\n[1] Hendy\, A.~S. and Van Bockstal\, K. On a reconstruction of a sol
ely time-dependent source in a time-fractional diffusion equation with non
-smooth solutions\, J. Sci. Comput.\, vol. 90\, Art. no. 1\, 2022.\n\n[2]
Hendy\, A.~S. and Van Bockstal\, K. A solely time-dependent source reconst
ruction in a multiterm time-fractional order diffusion equation with non-s
mooth solutions\, Numer. Algorithms\, vol. 90\, Art. no. 2\, 2022.\n\nThe
meeting id and passcode will be emailed to the seminar mailing list. For m
ore information please visit our webpage: www.inverseproblemseminars.com\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Bondarenko (Saratov State University)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/14
DESCRIPTION:Title: Inverse spectral problem for the third-order differential
operators with distribution coefficients\nby Natalia Bondarenko (Sarat
ov State University) as part of Seminars on Inverse Problems Theory and Ap
plications\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Kaltenbacher (University of Klagenfurt)
DTSTART:20231128T153000Z
DTEND:20231128T163000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/15
DESCRIPTION:Title: Coefficient identification in a space-fractional equation
with Abel type operators\nby Barbara Kaltenbacher (University of Klage
nfurt) as part of Seminars on Inverse Problems Theory and Applications\n\n
\nAbstract\nWe consider the inverse problem of recovering an unknown\, spa
tially-dependent coefficient $q(x)$ from the fractional order equation $\\
mathbb{L}_\\alpha u = f$ defined in a region of $\\real^2$ from boundary i
nformation. Here $\\mathbb{L_\\alpha} ={D}^{\\alpha_x}_x +{D}^{\\alpha_y}_
y +q(x)$\nwhere the operators ${D}^{\\alpha_x}_x$\, ${D}^{\\alpha_y}_y$ de
note fractional derivative operators based on the Abel fractional integral
. In the classical case this reduces to $-\\triangle u + q(x)u = f$ and th
is has been a well-studied problem. We develop both uniqueness and reconst
ruction results and show how the ill-conditioning of this inverse problem
depends on the geometry of the region and the fractional powers $\\alpha_x
$ and $\\alpha_y$.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Biljana Vojvodic (University of Banja Luka)
DTSTART:20231226T130000Z
DTEND:20231226T140000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/16
DESCRIPTION:Title: Inverse problems for operators with two delays - the bound
ary line between uniqueness and nonuniqueness of the solution\nby Bilj
ana Vojvodic (University of Banja Luka) as part of Seminars on Inverse Pro
blems Theory and Applications\n\n\nAbstract\nWe study the inverse spectral
problems of recovering operators with two constant delays $a_1$\, $a_2$ s
uch that $frac{\\pi}{3} \\leq a_1 < a_2 \\leq \\pi$\, for two types of ope
rators: Sturm--Liouville and Dirac differential operators. It is known tha
t the point $\\frac{2\\pi}{5}$ is of crucial importance for the operators
with one constant delay\, since for the delay not less than $\\frac{2\\pi}
{5}$ the theorem of uniqueness is true and otherwise it is not. For the op
erators with two delays\, it is much more complex to determine the boundar
y line which separates sets of validity and invalidity of the theorem of u
niqueness. We have proved that this boundary line is $2a_1+\\frac{a_2}{2}=
\\pi$ which represents the generalization of the results for the operators
with one delay.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Briceyda B. Delgado (INFOTEC\, Aguascalientes\, Mexico)
DTSTART:20240130T130000Z
DTEND:20240130T140000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/17
DESCRIPTION:Title: An inverse Sturm--Liouville problem on the half-line\n
by Briceyda B. Delgado (INFOTEC\, Aguascalientes\, Mexico) as part of Semi
nars on Inverse Problems Theory and Applications\n\n\nAbstract\nWe conside
r an inverse Sturm--Liouville problem on the half line. We show that the n
umerical solution of the problem is reduced to a system of linear algebrai
c equations\, using a Fourier-Legendre series representation of the transm
utation integral kernel as well as the Gel'fand-Levitan equation [1]. We c
lose the talk by giving a summary of other methods that have recently been
used for the analysis of this kind of inverse problems [2]. \n\nReference
s: \n\n[1] B. B. Delgado\, K. V. Khmelnytskaya\, V. V. Kravchenko\, The tr
ansmutation operator method for efficient solution of the inverse Sturm--L
iouville problem on the half-line\, Math. Meth. Appl. Sci.\, 42 (18)\, 735
9--7366\, 2019. \n\n[2] V. V. Kravchenko\, Direct and Inverse Sturm--Liouv
ille problems: A method of solution\, Birkhauser\, 2020.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Gernandt (University of Wuppertal)
DTSTART:20240227T130000Z
DTEND:20240227T140000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/18
DESCRIPTION:Title: A Calderón type inverse problem for tree graphs\nby H
annes Gernandt (University of Wuppertal) as part of Seminars on Inverse Pr
oblems Theory and Applications\n\n\nAbstract\nIn this talk\, we study the
inverse problem of recovering a metric tree from the knowledge of the Diri
chlet-to-Neumann matrix associated with the Laplacian. We prove an explici
t formula which relates this matrix to the pairwise weighted distances of
the leaves of the tree and\, thus\, allows us to recover the weighted tree
. This result can be viewed as a counterpart of the Calderón problem in t
he analysis of PDEs. In contrast to earlier results on inverse problems fo
r metric graphs\, we only assume knowledge of the Dirichlet-to-Neumann mat
rix for a fixed energy\, not of a whole matrix-valued function.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Pallikarakis (National Technical University of Athens)
DTSTART:20240326T130000Z
DTEND:20240326T140000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/19
DESCRIPTION:Title: Exploring Inverse Eigenvalue Problems through Machine Lear
ning\nby Nikolaos Pallikarakis (National Technical University of Athen
s) as part of Seminars on Inverse Problems Theory and Applications\n\n\nAb
stract\nThe latest years\, machine learning has been one of the main direc
tions in the numerical solution of inverse problems\, aiming to face the i
ll-posed nature of these problems. In this talk\, we delve into the numeri
cal solution of inverse eigenvalue problems from a machine learning perspe
ctive\, focusing on the inverse Sturm--Liouville eigenvalue problem for sy
mmetric potentials and the inverse transmission eigenvalue problem for sph
erically symmetric refractive indices. Firstly\, we formulate these eigenv
alue problems and pose the numerical solution of the corresponding direct
problems\, using well-known numerical methods. Next\, we present the main
ideas behind the supervised machine learning regression and briefly discus
s the basic properties of the algorithms we implement\, which are $k$-Near
est Neighbours (kNN)\, Random Forests (RF) and Neural Networks (MLP). Afte
rwards\, we numerically solve the direct problems and create the spectral
data which in turn are used as training data for the machine learning mode
ls. We consider examples of inverse problems and compare the performance o
f each model to predict the unknown potentials and refractive indices resp
ectively\, from a given small set of the lowest eigenvalues. Our experimen
ts validate the efficiency of these machine learning models for numericall
y solving inverse eigenvalue problems\, providing a proof-of-concept for t
heir applicability in this field.\n\n[1] N. Pallikarakis and A. Ntargaras\
, Application of machine leraning regression models to inverse eigenvalue
problems\, Computers & Mathematics with Applications\, 154\, 2024.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigorii Agafonkin (Lomonosov Moscow State University)
DTSTART:20240430T130000Z
DTEND:20240430T140000Z
DTSTAMP:20260404T110745Z
UID:inverseproblems/20
DESCRIPTION:Title: Construction of a potential for given essential spectrum o
f the singular Schrodinger operator on the half-line\nby Grigorii Aga
fonkin (Lomonosov Moscow State University) as part of Seminars on Inverse
Problems Theory and Applications\n\n\nAbstract\nWe consider the singular s
emibounded self-adjoint Shr\\"odinger operator acting in $L_2([0\,+\\infty
))$ formally defined as\n\\begin{gather*}\n H = -\\frac{\\\,d^2}{\\\,dx^2}
+ \\sum_{k=1}^{+\\infty}a_k\\delta_{x_k}\,\\\\\n D(H) = \\left\\{u \\in W
_2^2([0\,+\\infty)\\setminus\\{x_k\, \\ k\\in\\mathbb{N}\\}) \\cap C([0\,+
\\infty)) \\ : \\ u(0) = 0 \\right\\}\,\n\\end{gather*}\nwhere $a_k \\in \
\mathbb{R}$\, $x_k$ is an increasing sequence of positive real numbers and
$\\delta_{y}$ denotes the Dirac delta function supported at $y$. \n\nWe p
rove constructively that for every closed semi-bounded set $S \\subset \\m
athbb{R}$ one can always choose the values of parameters $a_k$ and $x_k$ s
uch that the essential spectrum of the operator $H$ coincides with the set
$S$. \n\nWe will also show how the same approach can also be applied to t
he operator in $L_2([0\,+\\infty))$ of the form\n\\begin{gather*}\n L = -\
\frac{\\\,d^2}{\\\,dx^2} + \\sum_{k=1}^{+\\infty}a_k\\chi_{[x_{k-1}\, x_k]
}\,\\\\\n D(L) = \\left\\{u \\in W_2^2([0\,+\\infty)) \\ : \\ u(0) = 0 \\r
ight\\}\,\n\\end{gather*}\n(where $\\chi_A$ stands for the characteristic
function of the set $A$).\n\nIn both cases the boundary condition at $0$ c
an be chosen Neumann instead of Dirichlet without affecting the main resul
t. \n\nA support from the Russian Science Foundation grant №20-11-20261
is acknowledged.\n
LOCATION:https://stable.researchseminars.org/talk/inverseproblems/20/
END:VEVENT
END:VCALENDAR