Search Results - "Numerical solution to inverse problems in abstract spaces"

A rotation total variation regularization for full waveform inversion

Authors: Faxuan Wu Qinglong He Jiangyan Zou et al.

Source: Journal of Inverse and Ill-posed Problems.

Subject Terms: full waveform inversion, inverse problems, rotation TV regularization, Numerical solution to inverse problems in abstract spaces, CGOPT algorithm, acoustic wave equation

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Access URL: https://zbmath.org/8025007
https://doi.org/10.1515/jiip-2022-0067

Robustness and exploration of variational and machine learning approaches to inverse problems: An overview: Robustness and exploration of variational and machine learning approaches to inverse problems: an overview

Authors: Alexander Auras Kanchana Vaishnavi Gandikota Hannah Droege et al.

Source: GAMM-Mitteilungen. 47

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, inverse problems, Computer Vision and Pattern Recognition (cs.CV), Image and Video Processing (eess.IV), Learning and adaptive systems in artificial intelligence, Computer Science - Computer Vision and Pattern Recognition, Numerical solution to inverse problems in abstract spaces, robustness, Numerical Analysis (math.NA), 02 engineering and technology, Electrical Engineering and Systems Science - Image and Video Processing, explorability, 01 natural sciences, Machine Learning (cs.LG), machine learning, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Mathematics - Numerical Analysis, Image processing (compression, reconstruction, etc.) in information and communication theory, 0101 mathematics

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Access URL: http://arxiv.org/abs/2402.12072
https://zbmath.org/7968740
https://doi.org/10.1002/gamm.202470003

Projection based summation-by-parts methods, embeddings and the pseudoinverse

Authors: Pelle Olsson Gustav Eriksson Ken Mattsson

Source: Journal of Computational Physics. 524:113689

Subject Terms: high-order accuracy, Beräkningsmatematik, projection method, Numerical solution to inverse problems in abstract spaces, stability, High-order accuracy, Computational Mathematics, Finite difference methods, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Projection method, boundary treatment, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability, finite difference methods, Boundary treatment

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Access URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-546211

Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type

Authors: Kai Zhu Min Zhong

Source: Inverse Problems. 41:035007

Subject Terms: Biomedical imaging and signal processing, Numerical aspects of computer graphics, image analysis, and computational geometry, non-smooth penalty, iterative regularization, Numerical solution to inverse problems in abstract spaces, acousto-electric tomography

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Access URL: https://zbmath.org/7988277
https://doi.org/10.1088/1361-6420/adb3c4

Uncertainty quantification for DeepONets with ensemble Kalman inversion: Uncertainty quantification for DeepONet with ensemble Kalman inversion

Authors: Andrew Pensoneault Xueyu Zhu

Source: Journal of Computational Physics. 523:113670

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, uncertainty quantification, Computer Science - Artificial Intelligence, Numerical solution to inverse problems in abstract spaces, Machine Learning (stat.ML), Numerical Analysis (math.NA), Inference from stochastic processes and prediction, ensemble Kalman inversion, Machine Learning (cs.LG), operator learning, Artificial Intelligence (cs.AI), Statistics - Machine Learning, FOS: Mathematics, Mathematics - Numerical Analysis, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2403.03444
https://zbmath.org/7986892
https://doi.org/10.1016/j.jcp.2024.113670

Optimization methods in inverse problems and applications to science and engineering

Authors: D. La Torre M. Ruiz Galán Herb Kunze

Source: Optimization and Engineering. 22:2151-2158

Subject Terms: Fractals, Inverse problems involving ordinary differential equations, 0211 other engineering and technologies, 0202 electrical engineering, electronic engineering, information engineering, Numerical solution to inverse problems in abstract spaces, 02 engineering and technology, Variational inequalities, Numerical solution of inverse problems involving ordinary differential equations, Numerical analysis

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Access URL: https://link.springer.com/content/pdf/10.1007/s11081-021-09688-y.pdf
https://link.springer.com/content/pdf/10.1007/s11081-021-09688-y.pdf
https://link.springer.com/article/10.1007/s11081-021-09688-y

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure: GrainGNN: a dynamic graph neural network for predicting 3D grain microstructure

Authors: Yigong Qin Stephen DeWitt Balasubramaniam Radhakrishnan et al.

Source: Journal of Computational Physics. 510:113061

Subject Terms: FOS: Computer and information sciences, deep learning, graph neural network, Numerical solution to inverse problems in abstract spaces, 02 engineering and technology, grain microstructure evolution, phase field simulations, 01 natural sciences, Computational Engineering, Finance, and Science (cs.CE), Computer-aided design (modeling of curves and surfaces), 0103 physical sciences, Computer Science - Computational Engineering, Finance, and Science, 0210 nano-technology, additive manufacturing

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Access URL: http://arxiv.org/abs/2401.03661

Parallel ensemble Kalman method with total variation regularization for large-scale field inversion

Authors: Zhang, Xin-Lei Zhang, Lei He, Guowei

Source: Journal of Computational Physics. 509:113059

Subject Terms: Numerical optimization and variational techniques, machine learning, parallel implementation, field inversion, Numerical solution to inverse problems in abstract spaces, ensemble Kalman method, data assimilation, Probabilistic models, generic numerical methods in probability and statistics

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Access URL: https://zbmath.org/8021020
https://doi.org/10.1016/j.jcp.2024.113059

Convergence of non-linear diagonal frame filtering for regularizing inverse problems

Authors: Andrea Ebner Markus Haltmeier

Source: Inverse Problems. 40:055009

Subject Terms: Signal theory (characterization, reconstruction, filtering, etc.), Linear operators and ill-posed problems, regularization, Numerical solutions of ill-posed problems in abstract spaces, regularization, Tikhonov regularization, Hilbert space, singular value decomposition, linear inverse problem, Numerical solution to inverse problems in abstract spaces, General harmonic expansions, frames, Numerical Analysis (math.NA), 01 natural sciences, Bregman distance, diagonal frame decomposition, FOS: Mathematics, plug-and-play regularization, Mathematics - Numerical Analysis, 0101 mathematics, non-linear frame-based filtering

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Access URL: http://arxiv.org/abs/2308.15666

Accelerating inverse inference of ensemble Kalman filter via reduced-order model trained using adaptive sparse observations

Authors: Yuepeng Wang Jie Li Wenju Zhao et al.

Source: Journal of Computational Physics. 496:112600

Subject Terms: reduced-order model (ROM), uncertainty quantification (UQ), Numerical solution to inverse problems in abstract spaces, data assimilation (DA), ensemble Kalman filter (EnKF), sparse observations

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Basis-to-basis operator learning using function encoders

Authors: Tyler Ingebrand Adam J. Thorpe Somdatta Goswami et al.

Source: Computer Methods in Applied Mechanics and Engineering. 435:117646

Subject Terms: FOS: Computer and information sciences, operator learning, Computer Science - Machine Learning, function encoders, Learning and adaptive systems in artificial intelligence, PDE modeling, Numerical solution to inverse problems in abstract spaces, neural operators, Machine Learning (cs.LG)

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Access URL: http://arxiv.org/abs/2410.00171
https://zbmath.org/7996076
https://doi.org/10.1016/j.cma.2024.117646

Replica Exchange Preconditioned Crank-Nicolson Langevin Dynamic MCMC Method with Multi-Variance Strategy for Bayesian Inverse Problems: A replica exchange preconditioned Crank-Nicolson Langevin dynamic MCMC method with multi-variance strategy for Bayesian inverse problems

Authors: Na Ou Zecheng Zhang Guang Lin

Source: Journal of Computational Physics. 510:113067

Subject Terms: Bayesian inverse problem, preconditioned Crank-Nicolson scheme, Numerical solution to inverse problems in abstract spaces, Numerical analysis or methods applied to Markov chains, Langevin diffusion, replica exchange Monte Carlo

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Access URL: https://zbmath.org/8021033
https://doi.org/10.1016/j.jcp.2024.113067

The fractional Laplacian based image inpainting

Authors: Lian, Xiangkai Fu, Qiang Su, Weijie et al.

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

Subject Terms: Numerical optimization and variational techniques, Variational methods applied to PDEs, variational methods, Numerical solution to inverse problems in abstract spaces, fractional Laplacian, Image processing (compression, reconstruction, etc.) in information and communication theory, PDE constrained optimization (numerical aspects), image inpainting, Fractional partial differential equations

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Access URL: https://zbmath.org/7815410
https://doi.org/10.3934/ipi.2023035

Adaptive Wavelet Galerkin Methods for Linear Inverse Problems: Adaptive wavelet Galerkin methods for linear inverse problems

Authors: Cohen, Albert Hoffmann, Marc Reiß, Markus

Source: SIAM Journal on Numerical Analysis. 42:1479-1501

Subject Terms: nonlinear methods, ddc:330, 330 Wirtschaft, Numerical solution to inverse problems in abstract spaces, Numerical methods for integral equations, wavelets, 01 natural sciences, Galerkin methods, numerical example, Numerical solutions to equations with linear operators, Besov spaces, Numerical methods for wavelets, statistical inverse problems, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), 0101 mathematics, minimax estimation, singular integral equation, Equations and inequalities involving linear operators, with vector unknowns

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Access URL: https://edoc.hu-berlin.de/bitstream/18452/4148/1/50.pdf
https://zbmath.org/2139932
https://doi.org/10.1137/s0036142902411793
http://hdl.handle.net/10419/65296
https://www.econstor.eu/bitstream/10419/65296/1/726723541.pdf

Direct and inverse computation of Jacobi matrices of infinite iterated function systems

Authors: MANTICA, GIORGIO DOMENICO PIO

Source: Numerische Mathematik. 125:705-731

Subject Terms: almost periodicity, numerical examples, algorithm, Jacobi (tridiagonal) operators (matrices) and generalizations, Other matrix algorithms, infinite iterated function system, inverse/approximation problem, FOS: Physical sciences, Numerical solution to inverse problems in abstract spaces, Numerical Analysis (math.NA), Mathematical Physics (math-ph), 42C05 47B36 65D32 65J22 81Q10, Numerical quadrature and cubature formulas, 01 natural sciences, Mathematics - Spectral Theory, Jacobi matrix, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, singularity of the measures, logarithmic capacity, Spectral Theory (math.SP), Mathematical Physics

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Access URL: http://arxiv.org/pdf/1106.4945
http://arxiv.org/abs/1106.4945
https://arxiv.org/abs/1106.4945
https://ui.adsabs.harvard.edu/abs/2011arXiv1106.4945M/abstract
https://arxiv.org/pdf/1106.4945v1
https://dblp.uni-trier.de/db/journals/nm/nm125.html#Mantica13
https://core.ac.uk/display/53559751
https://doi.org/10.1007/s00211-013-0551-7
https://rd.springer.com/article/10.1007/s00211-013-0551-7
https://link.springer.com/article/10.1007/s00211-013-0551-7
https://link.springer.com/article/10.1007/s00211-013-0551-7/fulltext.html

On an inverse problem: Recovery of non-smooth solutions to backward heat equation: On an inverse problem: recovery of non-smooth solutions to backward heat equation

Authors: Oscar Orellana Prabir Daripa Fabien Ternat

Source: Applied Mathematical Modelling. 36:4003-4019

Subject Terms: non-smooth solutions, heat equation, quasi-reversibility techniques, inverse problem, Numerical solution to inverse problems in abstract spaces, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, illposed problem, 0101 mathematics, finite difference methods, 01 natural sciences

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Access URL: https://zbmath.org/6114239
https://doi.org/10.1016/j.apm.2011.11.020
http://math.tamu.edu/~prabir.daripa/pubs/reprints/amm-2012.pdf
https://www.sciencedirect.com/science/article/pii/S0307904X11007086

A sparsity-constrained sampling method with applications to communications and inverse scattering

Authors: I. Harris J.D. Rezac

Source: Journal of Computational Physics. 451:110890

Subject Terms: Inverse problems for PDEs, inverse problems, Hydro- and aero-acoustics, Numerical solution to inverse problems in abstract spaces, acoustic scattering, 02 engineering and technology, 01 natural sciences, beamforming, array processing, Mathematics - Analysis of PDEs, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Inverse problems (including inverse scattering) in optics and electromagnetic theory, 0101 mathematics, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/pdf/2010.08032
http://arxiv.org/abs/2010.08032
https://zbmath.org/7517173
https://doi.org/10.1016/j.jcp.2021.110890

Discretized Tikhonov–Phillips regularization for a naturally linearized parameter identification problem: Discretized Tikhonov-Phillips regularization for a naturally linearized parameter identification problem

Authors: Hui Cao

Source: Journal of Complexity. 21:864-877

Subject Terms: Adaptive strategy, Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Parameter identification, Numerical methods for inverse problems for boundary value problems involving PDEs, diffusion equation, Applied Mathematics, Tikhonov–Phillips regularization, Numerical solution to inverse problems in abstract spaces, Tikhonov-Phillips regularization, 01 natural sciences, parameter identification, Boundary value problems for second-order elliptic equations, Natural linearization, linear ill-posed operator equation, Ill-posed problems for PDEs, natural linearization, adaptive strategy, 0101 mathematics

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Access URL: https://zbmath.org/2240098
https://doi.org/10.1016/j.jco.2005.04.003
https://www.sciencedirect.com/science/article/pii/S0885064X05000324
https://core.ac.uk/display/82777301
https://dblp.uni-trier.de/db/journals/jc/jc21.html#Cao05

Preconditioning Landweber iteration in Hilbert scales

Authors: Herbert Egger Andreas Neubauer

Source: Numerische Mathematik. 101:643-662

Subject Terms: Landweber iteration, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, preconditioning, Numerical solutions to equations with nonlinear operators, Numerical solutions to equations with linear operators, Nonlinear ill-posed problems, Numerical solution to inverse problems in abstract spaces, numerical results, 0101 mathematics, ill-posed inverse problems, Hilbert scales, 01 natural sciences

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On Efficient Computation of the Optimization Problem Arising in the Inverse Modeling of Non-Stationary Multiphase Multicomponent Flow Through Porous Media: On efficient computation of the optimization problem arising in the inverse modeling of non-stationary multiphase multicomponent flow through porous media

Authors: Volker Schulz Subhendu Bikash Hazra

Source: Computational Optimization and Applications. 31:69-85

Subject Terms: Inverse problems in optimal control, Control/observation systems governed by partial differential equations, Flows in porous media, filtration, seepage, multiphase flow, reduced Gauss-Newton technique, 0207 environmental engineering, multiple shooting, Numerical solution to inverse problems in abstract spaces, numerical parameter identification, 02 engineering and technology, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2193581
https://doi.org/10.1007/s10589-005-1052-0
https://link.springer.com/article/10.1007/s10589-005-1052-0
https://link.springer.com/10.1007/s10589-005-1052-0
https://dblp.uni-trier.de/db/journals/coap/coap31.html#HazraS05