Solving the Coefficient Inverse Problem by the Deep Galerkin Method

2021 ◽  
Author(s):  
Iryna Vergunova ◽  
Viktor Vergunov ◽  
Iuliia Rosemann
Keyword(s):  
Inverse Problem ◽  
Galerkin Method ◽  
Coefficient Inverse Problem

scholarly journals A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

2018 ◽  
Vol 11 (4) ◽  
pp. 2339-2367 ◽  
Author(s):  
Michael V. Klibanov ◽  
Nikolay A. Koshev ◽  
Dinh-Liem Nguyen ◽  
Loc H. Nguyen ◽  
Aaron Brettin ◽  
...  
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Numerical Method ◽  
Coefficient Inverse Problem ◽  
Single Measurement

scholarly journals Convexification for a 1D hyperbolic coefficient inverse problem with single measurement data

2020 ◽  
Vol 14 (5) ◽  
pp. 913-938 ◽  
Author(s):  
Alexey Smirnov ◽  
◽  
Michael Klibanov ◽  
Loc Nguyen
Keyword(s):  
Inverse Problem ◽  
Measurement Data ◽  
Coefficient Inverse Problem ◽  
Single Measurement

Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem

2010 ◽  
Vol 26 (4) ◽  
pp. 045003 ◽  
Author(s):  
Michael V Klibanov ◽  
Michael A Fiddy ◽  
Larisa Beilina ◽  
Natee Pantong ◽  
John Schenk
Keyword(s):  
Inverse Problem ◽  
Experimental Verification ◽  
Coefficient Inverse Problem ◽  
Globally Convergent ◽  
Convergent Algorithm

scholarly journals Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm

2017 ◽  
Vol 345 ◽  
pp. 17-32 ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Michael V. Klibanov ◽  
Loc H. Nguyen ◽  
Aleksandr E. Kolesov ◽  
Michael A. Fiddy ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Coefficient Inverse Problem ◽  
Raw Data ◽  
Globally Convergent ◽  
Convergent Algorithm

scholarly journals On the existence and uniqueness of the solution of the coefficient inverse problem for a semilinear parabolic equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012008
Author(s):  
A L Sugezhik
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Source Function ◽  
Semilinear Parabolic Equation ◽  
Coefficient Inverse Problem ◽  
Uniqueness Of The Solution ◽  
Bounded Functions ◽  
Semilinear Parabolic

Abstract In this paper, we consider the problem of determining the source function and the coefficient by the derivative with respect to time in a semilinear parabolic equation with overdetermination conditions defined on two different hyperplanes. The existence and uniqueness theorems of the classical solution of the posed coefficient inverse problem in the class of smooth bounded functions were proved. An example of input data satisfying the conditions of the proved theorems is given.

scholarly journals Reproducing kernel Hilbert space method for solutions of a coefficient inverse problem for the kinetic equation

2018 ◽  
Vol 8 (2) ◽  
pp. 145-151 ◽  
Author(s):  
Esra Karatas Akgül
Keyword(s):  
Hilbert Space ◽  
Inverse Problem ◽  
Kinetic Equation ◽  
Inverse Problems ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Approximate Solutions ◽  
Kernel Functions ◽  
Coefficient Inverse Problem ◽  
Space Method

On the basis of a reproducing kernel Hilbert space, reproducing kernel functions for solving the coefficient inverse problem for the kinetic equation are given in this paper. Reproducing kernel functions found in the reproducing kernel Hilbert space imply that they can be considered for solving such inverse problems. We obtain approximate solutions by reproducing kernel functions. We show our results by a table. We prove the eciency of the reproducing kernel Hilbert space method for solutions of a coefficient inverse problem for the kinetic equation.

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