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BEGIN:VEVENT
SUMMARY:Sergey Buterin\, Nebojsa Djuric
DTSTART:20220308T140000Z
DTEND:20220308T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/1
DESCRIPTION:Title: Inverse spectral problems for Dirac operators withconstant delay:
uniqueness\, characterization\, uni-form stability\nby Sergey Buterin\
, Nebojsa Djuric as part of Seminars on Inverse Problems Theory and Applic
ations\n\n\nAbstract\nWe initiate studying inverse spectral problems for D
irac-type functional-differential operators with constant delay. For simpl
icity\, we restrict ourselves to the case when the delay parameter is not
less than one-half of the interval. For the considered case\, however\, we
give answers to the full range of questions usually raised in the inverse
spectral theory. Specifically\, reconstruction of two complex $L_2$-poten
tials is studied from either complete spectra or subspectra of two boundar
y value problems with one common boundary condition. We give conditions on
the subspectra that are necessary and sufficient for the unique determina
tion of the potentials. Moreover\, necessary and sufficient conditions for
the solvability of both inverse problems are obtained. For the inverse pr
oblem involving the complete spectra\, we establish also uniform stability
in each ball of a finite radius. For this purpose\, we use recent results
on uniform stability of sine-type functions with asymptotically separated
zeros.\n
LOCATION:https://researchseminars.org/talk/inverseproblems/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Per Christian Hansen (Technical University of Denmark)
DTSTART:20220419T140000Z
DTEND:20220419T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/2
DESCRIPTION:Title: IR Tools: Iterative Regularization for Inverse Prob- lems\nby
Per Christian Hansen (Technical University of Denmark) as part of Seminars
on Inverse Problems Theory and Applications\n\n\nAbstract\nThe Matlab pac
kage IR Tools provides implementations of a range of\niterative solvers fo
r linear inverse problems\, and a set of large-scale test\nproblems in the
form of discretizations of 2D linear inverse problems.\nWe include iterat
ive regularization methods where the regularization is\ndue to the semi-co
nvergence\, and Tikhonov-type formulations where\nthe regularization is du
e to a regularization term. In both cases\, we can\nimpose bound constrain
ts on the solution. We implemented the iterative\nmethods in a flexible fa
shion that allows the problem’s coefficient matrix\nto be available as a
(sparse) matrix\, a function handle\, or an object. The\nbasic call to al
l of the iterative methods requires only this matrix and the\nright-hand s
ide. Our codes automatically set default parameters of the\nstopping rules
\, regularization parameters\, etc.\; with an optional input\nstructure\,
the user has full control of any of these algorithm parameters.\nThe test
problems represent realistic large-scale problems found in image\nreconstr
uction and several other applications. These new test problems\nreplace th
e small and outdated test problems from 1994 in Regularization\nTools. The
basic call to all of the test problem generators produces a\nmatrix\, a r
ight-hand side and the corresponding exact solution. Similar\nto the itera
tive methods\, the user can use an optional input structure to\ncontrol sp
ecific features of the test problem.\nThis is joint work with Silvia Gazzo
la and James G. Nagy.\n
LOCATION:https://researchseminars.org/talk/inverseproblems/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Kuznetsova (Saratov State University)
DTSTART:20220503T140000Z
DTEND:20220503T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/3
DESCRIPTION:Title: Inverse problem for the Sturm–Liouville operators with frozen ar
gument\nby Maria Kuznetsova (Saratov State University) as part of Semi
nars on Inverse Problems Theory and Applications\n\n\nAbstract\nThe talk i
s devoted to recovering the Sturm–Liouville operator with frozen argumen
t from its spectrum. Unique solvability of this inverse problem depends on
the position of frozen argument and the boundary conditions. We compare d
ifferent approaches to the inverse problem and the corresponding results i
n two cases of rational and irrational frozen argument. Further\, we sugge
st a new unified approach to operators with frozen argument\, which is eff
ective in the both cases.\n\nApplying it\, we obtain new-type asymptotic f
ormulae completely characterizing the class of sequences that can be the s
pectra of the considered operators.\n\nThis talk is based on the paper: Ku
znetsova\, M. Necessary and sufficient conditions for the spectra of the S
turm–Liouville operators with frozen argument\, Applied Mathematics Lett
ers 131 (2022)\, article 108035.\n\nThe paper is available via the link ht
tps://authors.elsevier.com/a/1enGg3BGwfEDzY\n\nMeeting ID: 967 6835 8960\n
Passcode: 705810\n
LOCATION:https://researchseminars.org/talk/inverseproblems/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Rowlett (Chalmers University of Technology)
DTSTART:20220607T140000Z
DTEND:20220607T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/4
DESCRIPTION:Title: The mathematics of ``hearing the shape of a drum''\nby Julie R
owlett (Chalmers University of Technology) as part of Seminars on Inverse
Problems Theory and Applications\n\n\nAbstract\nHave you heard the questio
n "Can one hear the shape of a drum?" Do you know the answer? In 1966\, M.
Kac's article of the same title popularized the inverse isospectral probl
em for planar domains. Twenty-six years later\, Gordon\, Webb\, and Wolper
t demonstrated the answer\, but many naturally related problems remain ope
n today. We will discuss old and new results inspired by "hearing the shap
e of a drum."\n
LOCATION:https://researchseminars.org/talk/inverseproblems/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuncay Aktosun (University of Texas at Arlington)
DTSTART:20220920T140000Z
DTEND:20220920T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/5
DESCRIPTION:Title: The Marchenko inversion method for the derivative NLS system\n
by Tuncay Aktosun (University of Texas at Arlington) as part of Seminars o
n Inverse Problems Theory and Applications\n\n\nAbstract\nThe Marchenko me
thod is presented for the linear system associated with the derivative NLS
(nonlinear Schrödinger) system. The system of linear Marchenko integral
equations is derived in order to solve the corresponding inverse scatterin
g problem. Through the use of the inverse scattering transform\, solutions
are obtained for the derivative NLS system. Explicit solution formulas ar
e developed in closed form by using as input a pair of matrix triplets cor
responding to reflectionless scattering data.\n\n*The meeting id and passc
ode will be emailed to the seminar mailing list.\n\n** For more informatio
n please visit our webpage: https://www.inverseproblemseminars.com\n
LOCATION:https://researchseminars.org/talk/inverseproblems/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Pallikarakis (National Technical University of Athens)
DTSTART:20221004T140000Z
DTEND:20221004T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/6
DESCRIPTION:Title: Inverse Spectral Problems for Classic and Modified Transmission Ei
genvalues\nby Nikolaos Pallikarakis (National Technical University of
Athens) as part of Seminars on Inverse Problems Theory and Applications\n\
n\nAbstract\nResearch on transmission eigenvalues has been a very active t
opic in inverse scattering theory. In this talk\, we discuss about the inv
erse transmission eigenvalue problem for the spherically symmetric refract
ive index. We present some well-known uniqueness results for the continuou
s case [1]. Next\, we highlight the need to introduce modified problems an
d demonstrate the corresponding modified transmission eigenvalue problem [
2]. A new uniqueness result for the inverse problem is derived [3]. We con
clude by summarizing similarities and differences among inverse problems u
sing classic and modifed transmission eigenvalues.\n\n[1] Gintides D and P
allikarakis N\, The inverse transmission eigenvalue problem for a disconti
nuous refractive index\, Inverse Problems\, 33\, 2017.\n\n[2] Gintides D\,
Pallikarakis N and Stratouras K\, On the modified transmission eigenvalue
problem with an artificial metamaterial background\, Res. Math. Sci.\, 8\
, 2021\, (special issue on transmission eigenvalues).\n\n[3] Gintides D\,
Pallikarakis N and Stratouras K\, Uniqueness of a spherically symmetric re
fractive index from modified transmission eigenvalues\, Inverse Problems\,
38\, 2022.\n\nThe meeting id and passcode will be emailed to the seminar
mailing list. For more information please visit our webpage: https://www.i
nverseproblemseminars.com\n
LOCATION:https://researchseminars.org/talk/inverseproblems/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangfang Liu (Michigan Technical University)
DTSTART:20221018T140000Z
DTEND:20221018T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/7
DESCRIPTION:Title: Deterministic-Statistical Approach for an Inverse Acoustic Source
Problem using Multiple Frequency Limited Aperture Data\nby Yangfang Li
u (Michigan Technical University) as part of Seminars on Inverse Problems
Theory and Applications\n\n\nAbstract\nWe propose a deterministic-statisti
cal method for an inverse source problem using multiple frequency limited
aperture far field data. The direct sampling method is used to obtain a di
sc such that it contains the compact support of the source. The Dirichlet
eigenfunctions of the disc are used to expand the source function. Then th
e inverse problem is recast as a statistical inference problem for the exp
ansion coefficients and the Bayesian inversion is employed to reconstruct
the coefficients. The stability of the statistical inverse problem with re
spect to the measured data is justified in the sense of Hellinger distance
. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) algorithm
is implemented to explore the posterior density function of the unknowns.
Numerical examples show that the proposed method is effective for both sm
ooth and non-smooth sources given limited-aperture data.\n\nThe meeting id
and passcode will be emailed to the seminar mailing list. For more inform
ation please visit our webpage: https://www.inverseproblemseminars.com\n
LOCATION:https://researchseminars.org/talk/inverseproblems/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Onur Baysal (University of Malta)
DTSTART:20221101T140000Z
DTEND:20221101T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/8
DESCRIPTION:Title: A New Numerical Approach for Identifiying Source Function in a Pla
te Equation\nby Onur Baysal (University of Malta) as part of Seminars
on Inverse Problems Theory and Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/inverseproblems/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masatoshi Suzuki (Tokio Institute of Technology)
DTSTART:20221115T140000Z
DTEND:20221115T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/9
DESCRIPTION:Title: An inverse problem for a class of canonical systems with no indivi
sible intervals\nby Masatoshi Suzuki (Tokio Institute of Technology) a
s part of Seminars on Inverse Problems Theory and Applications\n\n\nAbstra
ct\nA Hamiltonian is a 2-by-2 positive semidefinite real symmetric matrix-
valued function defined on an interval whose components are locally integr
able. A canonical system is a first-order system of linear differential eq
uations parametrized by complex numbers associated with a given Hamiltonia
n. The solution of a canonical system gives an entire function of the Herm
ite–Biehler class.\n\nIn this talk\, we solve the inverse problem which
recovers a Hamiltonian from a given function E in the Hermite–Biehler cl
ass under some special assumptions on E.\n\nThe method of the solution is
similar to the solution of the inverse problem for strings given\nby M. G.
Krein but is different. We will also explain the difference.\n\nThe meeti
ng id and passcode will be emailed to the seminar mailing list. For more i
nformation please visit our webpage: https://www.inverseproblemseminars.co
m\n
LOCATION:https://researchseminars.org/talk/inverseproblems/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sehrish Javed (Comsats University Islamabad)
DTSTART:20221129T140000Z
DTEND:20221129T150000Z
DTSTAMP:20260422T225703Z
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://researchseminars.org/talk/inverseproblems/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. A. Yurko (Saratov State University)
DTSTART:20221206T140000Z
DTEND:20221206T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/11
DESCRIPTION:Title: Inverse problems for discrete operators\nby V. A. Yurko (Sara
tov State University) as part of Seminars on Inverse Problems Theory and A
pplications\n\n\nAbstract\nWe give a short review of results on inverse sp
ectral problems for wide classes of discrete operators. We start with the
simplest class of Jacobi operators. Then we will pay attention\non other m
ore complicated classes of discrete operators. We will use a unified appro
ach for studying different classes\nof discrete operators.\n\nThe meeting
id and passcode will be emailed to the seminar mailing list. For more inf
ormation please visit our webpage: https://www.inverseproblemseminars.com\
n
LOCATION:https://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:20260422T225703Z
UID:inverseproblems/12
DESCRIPTION:Title: Inverse spectral problem and Volterra type lattices\nby A.S.
Osipov (Scientific-Research Institute for System Analysis of the Russian A
cademy of Sciences) as part of Seminars on Inverse Problems Theory and App
lications\n\n\nAbstract\nIn this talk\, we mainly consider some issues rel
ated to the study of Volterra lattice (also known as Kac-van Moerbeke syst
em\, Langmuir chain or discrete Korteweg-de Vries equation) in the semi-in
finite case. In particular\, we consider its integration via Lax pair form
alism by means of the inverse spectral problem for (Jacobi-like) second or
der difference operators. The key role in this inverse problem integration
method is played by the moments of the Weyl function of the corresponding
difference operator\, which appears in the Lax representation for this la
ttice\, and their evolution in time. We discuss the extension of this meth
od to another classes of nonlinear dynamical systems (e.g. Bogoyavlensky l
attices) and their other applications to the theory of nonlinear integrabl
e equations. This talk is partly based on the following papers:\n\n[1] Osi
pov A.S. (2020) Inverse spectral problems for second-order difference oper
ators and their application to the study of Volterra type systems\, Rus. J
. Nonlin. Dyn.\, 16:3\, 397--419. (available at http://nd.ics.org.ru/nd200
301/ )\n\n[2] Osipov A.S. (2021) Inverse spectral problem for Jacobi opera
tors and Miura transformation\, Concr. Oper.\, 8:1\, 77--89.(available at
https://doi.org/10.1515/conop-2020-0116 )\n\n[3] Osipov A. S. (2022) Inver
se spectral problem for band operators and their sparsity criterion in ter
ms of inverse problems data\, Russian Journal of Mathematical Physics\, 29
:2\, 225--237.\n\nThe meeting id and passcode will be emailed to the semin
ar mailing list. For more information please visit our webpage: www.invers
eproblemseminars.com\n
LOCATION:https://researchseminars.org/talk/inverseproblems/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karel Van Bockstal (Ghent University)
DTSTART:20230307T140000Z
DTEND:20230307T150000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/13
DESCRIPTION:Title: Inverse source problem in time-fractional diffusion equations wit
h non-smooth solutions\nby Karel Van Bockstal (Ghent University) as pa
rt of Seminars on Inverse Problems Theory and Applications\n\n\nAbstract\n
This talk is based on the papers [1] and [2]. In [1]\, an inverse source p
roblem (ISP) for a time-fractional diffusion equation of order $\\alpha\\i
n(0\,1)$ is discussed. The missing solely time-dependent source is recover
ed from an additional integral measurement. An additional challenge is tha
t the coefficients of the elliptic operator considered are dependent on sp
atial and time variables. Two research questions are of concern in this ta
lk: (i) the existence and uniqueness of a (weak) solution to the ISP for e
xact data\, and (ii) the numerical reconstruction of the unknown source. M
oreover\, the extension of the results to multiterm time-fractional diffus
ion 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 solely tim
e-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 reconstruction
in a multiterm time-fractional order diffusion equation with non-smooth s
olutions\, Numer. Algorithms\, vol. 90\, Art. no. 2\, 2022.\n\nThe meeting
id and passcode will be emailed to the seminar mailing list. For more inf
ormation please visit our webpage: www.inverseproblemseminars.com\n
LOCATION:https://researchseminars.org/talk/inverseproblems/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Bondarenko (Saratov State University)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/14
DESCRIPTION:Title: Inverse spectral problem for the third-order differential operato
rs with distribution coefficients\nby Natalia Bondarenko (Saratov Stat
e University) as part of Seminars on Inverse Problems Theory and Applicati
ons\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/inverseproblems/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Kaltenbacher (University of Klagenfurt)
DTSTART:20231128T153000Z
DTEND:20231128T163000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/15
DESCRIPTION:Title: Coefficient identification in a space-fractional equation with Ab
el type operators\nby Barbara Kaltenbacher (University of Klagenfurt)
as part of Seminars on Inverse Problems Theory and Applications\n\n\nAbstr
act\nWe consider the inverse problem of recovering an unknown\, spatially-
dependent coefficient $q(x)$ from the fractional order equation $\\mathbb{
L}_\\alpha u = f$ defined in a region of $\\real^2$ from boundary informat
ion. Here $\\mathbb{L_\\alpha} ={D}^{\\alpha_x}_x +{D}^{\\alpha_y}_y +q(x)
$\nwhere the operators ${D}^{\\alpha_x}_x$\, ${D}^{\\alpha_y}_y$ denote fr
actional derivative operators based on the Abel fractional integral. In th
e classical case this reduces to $-\\triangle u + q(x)u = f$ and this has
been a well-studied problem. We develop both uniqueness and reconstruction
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://researchseminars.org/talk/inverseproblems/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Biljana Vojvodic (University of Banja Luka)
DTSTART:20231226T130000Z
DTEND:20231226T140000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/16
DESCRIPTION:Title: Inverse problems for operators with two delays - the boundary lin
e between uniqueness and nonuniqueness of the solution\nby Biljana Voj
vodic (University of Banja Luka) as part of Seminars on Inverse Problems T
heory and Applications\n\n\nAbstract\nWe study the inverse spectral proble
ms of recovering operators with two constant delays $a_1$\, $a_2$ such tha
t $frac{\\pi}{3} \\leq a_1 < a_2 \\leq \\pi$\, for two types of operators:
Sturm--Liouville and Dirac differential operators. It is known that the p
oint $\\frac{2\\pi}{5}$ is of crucial importance for the operators with on
e constant delay\, since for the delay not less than $\\frac{2\\pi}{5}$ th
e theorem of uniqueness is true and otherwise it is not. For the operators
with two delays\, it is much more complex to determine the boundary line
which separates sets of validity and invalidity of the theorem of uniquene
ss. We have proved that this boundary line is $2a_1+\\frac{a_2}{2}=\\pi$ w
hich represents the generalization of the results for the operators with o
ne delay.\n
LOCATION:https://researchseminars.org/talk/inverseproblems/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Briceyda B. Delgado (INFOTEC\, Aguascalientes\, Mexico)
DTSTART:20240130T130000Z
DTEND:20240130T140000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/17
DESCRIPTION:Title: An inverse Sturm--Liouville problem on the half-line\nby Bric
eyda B. Delgado (INFOTEC\, Aguascalientes\, Mexico) as part of Seminars on
Inverse Problems Theory and Applications\n\n\nAbstract\nWe consider an in
verse Sturm--Liouville problem on the half line. We show that the numerica
l solution of the problem is reduced to a system of linear algebraic equat
ions\, using a Fourier-Legendre series representation of the transmutation
integral kernel as well as the Gel'fand-Levitan equation [1]. We close th
e talk by giving a summary of other methods that have recently been used f
or the analysis of this kind of inverse problems [2]. \n\nReferences: \n\n
[1] B. B. Delgado\, K. V. Khmelnytskaya\, V. V. Kravchenko\, The transmuta
tion operator method for efficient solution of the inverse Sturm--Liouvill
e problem on the half-line\, Math. Meth. Appl. Sci.\, 42 (18)\, 7359--7366
\, 2019. \n\n[2] V. V. Kravchenko\, Direct and Inverse Sturm--Liouville pr
oblems: A method of solution\, Birkhauser\, 2020.\n
LOCATION:https://researchseminars.org/talk/inverseproblems/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Gernandt (University of Wuppertal)
DTSTART:20240227T130000Z
DTEND:20240227T140000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/18
DESCRIPTION:Title: A Calderón type inverse problem for tree graphs\nby Hannes G
ernandt (University of Wuppertal) as part of Seminars on Inverse Problems
Theory and Applications\n\n\nAbstract\nIn this talk\, we study the inverse
problem of recovering a metric tree from the knowledge of the Dirichlet-t
o-Neumann matrix associated with the Laplacian. We prove an explicit formu
la which relates this matrix to the pairwise weighted distances of the lea
ves 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 the anal
ysis of PDEs. In contrast to earlier results on inverse problems for metri
c graphs\, we only assume knowledge of the Dirichlet-to-Neumann matrix for
a fixed energy\, not of a whole matrix-valued function.\n
LOCATION:https://researchseminars.org/talk/inverseproblems/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Pallikarakis (National Technical University of Athens)
DTSTART:20240326T130000Z
DTEND:20240326T140000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/19
DESCRIPTION:Title: Exploring Inverse Eigenvalue Problems through Machine Learning\nby Nikolaos Pallikarakis (National Technical University of Athens) as p
art of Seminars on Inverse Problems Theory and Applications\n\n\nAbstract\
nThe latest years\, machine learning has been one of the main directions i
n the numerical solution of inverse problems\, aiming to face the ill-pose
d nature of these problems. In this talk\, we delve into the numerical sol
ution of inverse eigenvalue problems from a machine learning perspective\,
focusing on the inverse Sturm--Liouville eigenvalue problem for symmetric
potentials and the inverse transmission eigenvalue problem for sphericall
y symmetric refractive indices. Firstly\, we formulate these eigenvalue pr
oblems and pose the numerical solution of the corresponding direct problem
s\, using well-known numerical methods. Next\, we present the main ideas b
ehind the supervised machine learning regression and briefly discuss the b
asic properties of the algorithms we implement\, which are $k$-Nearest Nei
ghbours (kNN)\, Random Forests (RF) and Neural Networks (MLP). Afterwards\
, we numerically solve the direct problems and create the spectral data wh
ich in turn are used as training data for the machine learning models. We
consider examples of inverse problems and compare the performance of each
model to predict the unknown potentials and refractive indices respectivel
y\, from a given small set of the lowest eigenvalues. Our experiments vali
date the efficiency of these machine learning models for numerically solvi
ng inverse eigenvalue problems\, providing a proof-of-concept for their ap
plicability in this field.\n\n[1] N. Pallikarakis and A. Ntargaras\, Appli
cation of machine leraning regression models to inverse eigenvalue problem
s\, Computers & Mathematics with Applications\, 154\, 2024.\n
LOCATION:https://researchseminars.org/talk/inverseproblems/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigorii Agafonkin (Lomonosov Moscow State University)
DTSTART:20240430T130000Z
DTEND:20240430T140000Z
DTSTAMP:20260422T225703Z
UID:inverseproblems/20
DESCRIPTION:Title: Construction of a potential for given essential spectrum of the
singular Schrodinger operator on the half-line\nby Grigorii Agafonkin
(Lomonosov Moscow State University) as part of Seminars on Inverse Problem
s Theory and Applications\n\n\nAbstract\nWe consider the singular semiboun
ded self-adjoint Shr\\"odinger operator acting in $L_2([0\,+\\infty))$ for
mally defined as\n\\begin{gather*}\n H = -\\frac{\\\,d^2}{\\\,dx^2} + \\su
m_{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 $\\del
ta_{y}$ denotes the Dirac delta function supported at $y$. \n\nWe prove co
nstructively that for every closed semi-bounded set $S \\subset \\mathbb{R
}$ one can always choose the values of parameters $a_k$ and $x_k$ such tha
t 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 the oper
ator 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 \\right\\}
\,\n\\end{gather*}\n(where $\\chi_A$ stands for the characteristic functio
n of the set $A$).\n\nIn both cases the boundary condition at $0$ can be c
hosen Neumann instead of Dirichlet without affecting the main result. \n\n
A support from the Russian Science Foundation grant №20-11-20261 is ackn
owledged.\n
LOCATION:https://researchseminars.org/talk/inverseproblems/20/
END:VEVENT
END:VCALENDAR