A Direct Sampling Method and Its Integration with Deep Learning for Inverse Scattering Problems with Phaseless Data: A direct sampling method and its integration with deep learning for inverse scattering problems with phaseless data

Authors: Jianfeng Ning, Fuqun Han, Jun Zou

Source: SIAM Journal on Scientific Computing. 47:C343-C368

Subject Terms: Inverse problems for PDEs, direct sampling method, Numerical methods for inverse problems for boundary value problems involving PDEs, phaseless data, Scattering theory for PDEs, FOS: Mathematics, deep learning, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), inverse scattering problem, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2403.02584

Direct sampling method for solving the inverse acoustic wave scattering problems in the time domain

Authors: Guo, Hong, Huang, Jin, Li, Zhaoxing

Source: Computers & Mathematics with Applications. 179:229-242

Subject Terms: Fourier-Laplace transform, direct sampling method, acoustic wave, Numerical methods for inverse problems for boundary value problems involving PDEs, time domain, Hydro- and aero-acoustics, inverse scattering problem

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Uniqueness and numerical resolution via iterated sensitivity equation of an inverse electromagnetic coefficient problem with partial boundary data

Authors: Heleine, Jérémy

Source: Inverse Problems and Imaging. 19:498-522

Subject Terms: numerical simulations, Inverse problems for PDEs, Maxwell equations, Maxwell's equations, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse problem, uniqueness, sensitivity equation, quasi-reversibility, Numerical methods for ill-posed problems for boundary value problems involving PDEs

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Polarized consensus-based dynamics for optimization and sampling

Authors: Bungert, Leon, Roith, Tim, Wacker, Philipp

Source: Mathematical programming 21, 125-155 (2024). doi:10.1007/s10107-024-02095-y
Mathematical Programming

Subject Terms: PDEs in connection with control and optimization, polarization, sampling, Numerical methods for inverse problems for boundary value problems involving PDEs, Asymptotic behavior of solutions to PDEs, global optimization, 90C26, 35Q93, 35B40, 65N21, 02 engineering and technology, Numerical Analysis (math.NA), Nonconvex programming, global optimization, 01 natural sciences, consensus-based optimization, 49 - Mathematical sciences::4905 - Statistics::490503 - Computational statistics, Optimization and Control (math.OC), 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Numerical Analysis, 49 - Mathematical sciences::4903 - Numerical and computational mathematics::490304 - Optimisation, 0101 mathematics, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2211.05238
https://zbmath.org/8035682
https://doi.org/10.1007/s10107-024-02095-y
https://bib-pubdb1.desy.de/record/607321

Recovery of the rod cross-section shape

Authors: Vladislav V. Kravchenko, Sergii M. Torba, Alexander O. Vatulyan

Source: Boletín de la Sociedad Matemática Mexicana. 31

Subject Terms: Inverse problems for PDEs, Applications of boundary value problems involving ordinary differential equations, Numerical methods for inverse problems for boundary value problems involving PDEs, Inverse problems involving ordinary differential equations, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), FOS: Physical sciences, Numerical Analysis (math.NA), Mathematical Physics (math-ph), Sturm-Liouville theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Linear boundary value problems for ordinary differential equations, Wave equation, Mathematics - Numerical Analysis, Numerical solution of inverse problems involving ordinary differential equations, Mathematical Physics, 34A55, 34B05, 34B24, 34B60, 34L40, 35L05, 35R30, 65L09, 65N21

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Access URL: http://arxiv.org/abs/2502.12368
https://zbmath.org/8032038
https://doi.org/10.1007/s40590-025-00727-7

Existence and Uniqueness Results for Generalized Non-local Hallaire-Luikov Moisture Transfer Equation: Existence and uniqueness results for generalized non-local Hallaire-Luikov moisture transfer equation

Authors: Asim Ilyas, Salman A. Malik, Kamran Suhaib

Source: Acta Applicandae Mathematicae. 195

Subject Terms: Inverse problems for PDEs, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Inverse problems in thermodynamics and heat transfer, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse problem, Hallaire-Luikov moisture transfer equation, Fractional partial differential equations, ill-posedness, Hilfer derivative, Mittag-Leffer-type functions

File Description: application/xml

Access URL: https://zbmath.org/7991512
https://doi.org/10.1007/s10440-025-00712-2

Recovering the impedance function or shape of elastic obstacle from partial Cauchy data

Authors: Sun, Yao, Wang, Pan, Bo, Chen

Source: Discrete and Continuous Dynamical Systems - S. 17:2654-2678

Subject Terms: Cauchy data, Inverse problems for PDEs, Inverse problems for waves in solid mechanics, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse impedance problem, boundary integral equation, Overdetermined boundary value problems for PDEs and systems of PDEs, inverse shape problem, Navier equation, Boundary element methods applied to problems in solid mechanics

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Access URL: https://zbmath.org/7893924
https://doi.org/10.3934/dcdss.2024025

Reconstruction of Voronoi diagrams: the case of inverse conductivity problems

Authors: Ernesto G Birgin, Antoine Laurain, Danilo R Souza

Source: Inverse Problems. 41:055007

Subject Terms: Inverse problems for PDEs, Boundary value problems for second-order elliptic equations, non-smooth shape calculus, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse conductivity problems, Voronoi diagrams, optimization

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Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method: Crack identification in a multi-layer inhomogeneous domain using the reciprocity gap-linear sampling method

Authors: Yosra Boukari, Nouha Jenhani

Source: Inverse Problems. 41:045014

Subject Terms: Inverse problems for PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse problems, RG-LSM, crack identification, data completion algorithm, Helmholtz equation

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Multi-frequency progressive refinement for learned inverse scattering

Authors: Owen Melia, Olivia Tsang, Vasileios Charisopoulos, Yuehaw Khoo, Jeremy Hoskins, Rebecca Willett

Source: Journal of Computational Physics. 527:113809

Subject Terms: machine learning, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse problems, algorithm unrolling, deep learning, FOS: Physical sciences, inverse scattering, Computational Physics (physics.comp-ph), Physics - Computational Physics, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2405.13214

Fading regularization method for an inverse boundary value problem associated with the biharmonic equation

Authors: Boukraa, Mohamed Aziz, Caillé, Laëtitia, Delvare, Franck

Contributors: Boukraa, Mohamed Aziz, Inversion of Differential Equations For Imaging and physiX (IDEFIX), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF)-Centre Inria de l'Institut Polytechnique de Paris, Centre Inria de Saclay, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre Inria de Saclay, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Photomécanique et analyse expérimentale en mécanique des solides Institut Pprime (PEM), Département Génie Mécanique et Systèmes Complexes Institut Pprime (Département GMSC), Institut Pprime UPR 3346 (PPrime Poitiers ), Université de Poitiers = University of Poitiers (UP)-École Nationale Supérieure de Mécanique et d’Aérotechnique Poitiers (ISAE-ENSMA)-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers = University of Poitiers (UP)-École Nationale Supérieure de Mécanique et d’Aérotechnique Poitiers (ISAE-ENSMA)-Centre National de la Recherche Scientifique (CNRS)-Institut Pprime UPR 3346 (PPrime Poitiers ), Université de Poitiers = University of Poitiers (UP)-École Nationale Supérieure de Mécanique et d’Aérotechnique Poitiers (ISAE-ENSMA)-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers = University of Poitiers (UP)-École Nationale Supérieure de Mécanique et d’Aérotechnique Poitiers (ISAE-ENSMA)-Centre National de la Recherche Scientifique (CNRS), Franco-Tunisian Hubert Curien Program (PHC Utique -CMCU 20G1501- Campus France 44300SD)

Source: Journal of Computational and Applied Mathematics. 457:116285

Subject Terms: Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs, Cauchy problem, Numerical optimization and variational techniques, method of fundamental solutions, biharmonic equation, Numerical methods for inverse problems for boundary value problems involving PDEs, Partial functional-differential equations, [MATH] Mathematics [math], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Biharmonic equation, inverse boundary value problems, Inverse boundary value problems, Method of fundamental solutions, Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions, [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

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Access URL: https://zbmath.org/7958822
https://doi.org/10.1016/j.cam.2024.116285
https://hal.science/hal-04711339v1/document
https://hal.science/hal-04711339v1
https://doi.org/10.1016/j.cam.2024.116285

Imaging anisotropic conductivity from internal measurements with mixed least-squares deep neural networks

Authors: Siyu Cen, Bangti Jin, Xiyao Li, Zhi Zhou

Source: Journal of Computational Physics. 523:113648

Subject Terms: Numerical optimization and variational techniques, mixed least-squares, Numerical methods for inverse problems for boundary value problems involving PDEs, deep neural network, FOS: Mathematics, error estimate, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), anisotropic conductivity, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2412.00527

Extended-Sampling-Bayesian Method for Limited Aperture Inverse Scattering Problems: Extended-sampling-Bayesian method for limited aperture inverse scattering problems

Authors: Zhaoxing Li, Zhiliang Deng, Jiguang Sun

Source: SIAM Journal on Imaging Sciences. 13:422-444

Subject Terms: Numerical methods for inverse problems for boundary value problems involving PDEs, Bayesian inference, Inverse problems (including inverse scattering) in optics and electromagnetic theory, Hydro- and aero-acoustics, extended sampling method, Bayesian inversion, inverse scattering, limited aperture, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://epubs.siam.org/doi/pdf/10.1137/19M1270501
https://doi.org/10.1137/19M1270501
https://dblp.uni-trier.de/db/journals/siamis/siamis13.html#LiDS20

Full-waveform reconstruction of micro-seismic events via topological derivative approach

Authors: A.A.M. da Silva, A.A. Novotny, A.A.S. Amad, B.B. Guzina

Source: Journal of Computational Physics. 510:113099

Subject Terms: frequency-domain analysis, Physics - Geophysics, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, full waveform inversion, Numerical methods for inverse problems for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, acoustic emission, moment tensor inversion

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.08677
https://zbmath.org/8021056
https://doi.org/10.1016/j.jcp.2024.113099

A SBFEM and sensitivity analysis based algorithm for solving inverse viscoelastic problems

Authors: Wang Chongshuai, He Yiqian, Yang Haitian

Source: Engineering Analysis with Boundary Elements. 106:588-598

Subject Terms: Inverse problems in equilibrium solid mechanics, Numerical methods for inverse problems for boundary value problems involving PDEs, 02 engineering and technology, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 01 natural sciences, 0203 mechanical engineering, inverse problem, identification, derivative, 0101 mathematics, adaptive computing, Boundary element methods applied to problems in solid mechanics, viscoelasticity, scaled boundary finite element method (SBFEM)

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0955799719300633

An inverse dipole source problem in inhomogeneous media: Application to the EEG source localization in neonates: An inverse dipole source problem in inhomogeneous media: application to the EEG source localization in neonates

Authors: Darbas, Marion, Diallo, Mohamadou Malal, El Badia, Abdellatif, Lohrengel, Stephanie

Contributors: Laboratoire de Mathématiques de Reims (LMR), Université de Reims Champagne-Ardenne (URCA)-Centre National de la Recherche Scientifique (CNRS)

Source: Journal of Inverse and Ill-posed Problems. 27:255-281

Subject Terms: Biomedical imaging and signal processing, Identification in stochastic control theory, Numerical methods for inverse problems for boundary value problems involving PDEs, PDEs in connection with biology, chemistry and other natural sciences, stability, identifiability, 16. Peace & justice, 01 natural sciences, Least squares and related methods for stochastic control systems, inverse source problem, EEG, Sensitivity, stability, well-posedness, 0101 mathematics, numerical experiments, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

File Description: application/xml

Access URL: https://zbmath.org/7068273
https://doi.org/10.1515/jiip-2017-0120
http://www.degruyter.com/view/j/jiip.2019.27.issue-2/jiip-2017-0120/jiip-2017-0120.xml

Machine Learning of Space-Fractional Differential Equations: Machine learning of space-fractional differential equations

Authors: Mamikon Gulian, Maziar Raissi, Paris Perdikaris, George Karniadakis

Source: SIAM Journal on Scientific Computing. 41:A2485-A2509

Subject Terms: FOS: Computer and information sciences, matérn kernel, Computer Science - Machine Learning, 35R11, 65N21, 62M10, 62F15, 60G15, 60G52, Numerical methods for inverse problems for boundary value problems involving PDEs, Bayesian inference, fractional diffusion, Gaussian processes, Machine Learning (stat.ML), Fractional partial differential equations, 01 natural sciences, stable process, Machine Learning (cs.LG), Time series, auto-correlation, regression, etc. in statistics (GARCH), Stable stochastic processes, anomalous diffusion, Statistics - Machine Learning, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/pdf/1808.00931
http://arxiv.org/abs/1808.00931

Numerical method for inverse scattering by random penetrable periodic structures

Authors: Wang, Yi, Lv, Junliang, Li, Shuxin

Source: Inverse Problems and Imaging. 0:0-0

Subject Terms: Landweber iterative, Numerical methods for inverse problems for boundary value problems involving PDEs, Tikhonov regularization, penetrable periodic structures, Inverse problems (including inverse scattering) in optics and electromagnetic theory, muilti-frequency method, Monte Carlo methods, inverse scattering, stationary stochastic processes

File Description: application/xml

Access URL: https://zbmath.org/7977868
https://doi.org/10.3934/ipi.2024038

A novel direct Helmholtz solver in inhomogeneous media based on the operator Fourier transform functional calculus

Authors: Max Cubillos, Edwin Jimenez

Source: Journal of Computational Physics. 527:113808

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Functional calculus for linear operators, operator Fourier transform, 41A35, 47A60, 47G30, 65N99, 78A40, Numerical methods for inverse problems for boundary value problems involving PDEs, inhomogeneous media, FOS: Physical sciences, wave propagation, Numerical Analysis (math.NA), Computational Physics (physics.comp-ph), FOS: Mathematics, Mathematics - Numerical Analysis, Pseudodifferential operators, Waves and radiation in optics and electromagnetic theory, Helmholtz, Physics - Computational Physics

File Description: application/xml

Access URL: http://arxiv.org/abs/2407.09436
https://zbmath.org/8021106
https://doi.org/10.1016/j.jcp.2025.113808

Regularized Reduced Order Lippmann-Schwinger-Lanczos Method for Inverse Scattering Problems in the Frequency Domain: Regularized reduced order Lippmann-Schwinger-Lanczos method for inverse scattering problems in the frequency domain

Authors: J. Baker, E. Cherkaev, V. Druskin, S. Moskow, M. Zaslavsky

Source: Journal of Computational Physics. 525:113725

Subject Terms: Numerical methods for inverse problems for boundary value problems involving PDEs, FOS: Mathematics, reduced order model, Schrödinger equation, inverse scattering, Helmholtz equation, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Lippmann-Schwinger Lanczos algorithm

File Description: application/xml

Access URL: http://arxiv.org/abs/2311.16367
https://zbmath.org/8021062
https://doi.org/10.1016/j.jcp.2025.113725