Search Results - numerical (solution OR evolution) to inverse problems in abstract space

Approximation of inverse problems for fractional differential equations in abstract spaces

Authors: Santosh Ruhil Muslim Malik Kottakkaran Sooppy Nisar et al.

Source: Alexandria Engineering Journal, Vol 121, Iss , Pp 529-538 (2025)

Subject Terms: Inverse problems, Fractional differential equations, α-resolvent family, Optimal control, Approximation theory, Engineering (General). Civil engineering (General), TA1-2040

File Description: electronic resource

Relation: http://www.sciencedirect.com/science/article/pii/S1110016825002571; https://doaj.org/toc/1110-0168

Access URL: https://doaj.org/article/55d8a9aa6e80455595b7595918032d9b

Approximation of inverse problems for fractional differential equations in abstract spaces.

Authors: Ruhil, Santosh Malik, Muslim Nisar, Kottakkaran Sooppy et al.

Source: Alexandria Engineering Journal. May2025, Vol. 121, p529-538. 10p.

Subject Terms: Inverse problems, Optimization algorithms, Approximation theory, Hilbert space, Differential equations

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

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

File Description: application/xml

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

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

File Description: application/xml

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

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

Numerical Solution of Inverse Scattering Problems with Multi-experimental Limited Aperture Data: Numerical solution of inverse scattering problems with multi-experimental limited aperture data

Authors: Gang Bao Jun Liu

Source: SIAM Journal on Scientific Computing. 25:1102-1117

Subject Terms: Hilbert spaces, smooth nonlinear operator, Numerical solutions to equations with nonlinear operators, Nonlinear ill-posed problems, Numerical solution to inverse problems in abstract spaces, global minimum, multiple data, 01 natural sciences, global convergence, inverse medium problems, Inverse problems (including inverse scattering) in optics and electromagnetic theory, homotopy continuation, limited aperture, 0101 mathematics, recursive linearization

File Description: application/xml

Access URL: https://zbmath.org/2030260
https://doi.org/10.1137/s1064827502409705

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

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

File Description: application/xml

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

Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems

Authors: Freitag, Melina A Hofmann, B

Source: Freitag, M A & Hofmann, B 2005, 'Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems', Journal of Inverse and Ill-posed Problems, vol. 13, no. 2, pp. 123-148. https://doi.org/10.1515/1569394053978524

Subject Terms: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, Tikhonov regularization, name=Applied Mathematics, Numerical solution to inverse problems in abstract spaces, compact operator, ill-posed problem, multiplication operators, 01 natural sciences, Nemytskij operator, linear operator equations, Numerical solutions to equations with linear operators, 0101 mathematics

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Access URL: https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://zbmath.org/2204565
https://doi.org/10.1515/1569394053978524
https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://researchportal.bath.ac.uk/en/publications/analytical-and-numerical-studies-on-the-influence-of-multiplicati
https://core.ac.uk/display/2810776

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

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

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

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

A note on quasi-maximum likelihood solutions to an inverse problem for Poisson processes: A note on quasi-maximum likelihood solutions to an inverse problem for Poisson processes.

Authors: Zbigniew Szkutnik

Source: Statistics & Probability Letters. 60:253-263

Subject Terms: 0502 economics and business, 05 social sciences, Quasi-maximum likelihood, Numerical solution to inverse problems in abstract spaces, Point processes (e.g., Poisson, Cox, Hawkes processes), Poisson process, Intensity function, Unfolding, 0101 mathematics, Non-Markovian processes: estimation, 01 natural sciences, Discretization

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Access URL: https://zbmath.org/1907001
https://doi.org/10.1016/s0167-7152(02)00269-9
https://www.sciencedirect.com/science/article/abs/pii/S0167715202002699
https://econpapers.repec.org/RePEc:eee:stapro:v:60:y:2002:i:3:p:253-263
https://econpapers.repec.org/article/eeestapro/v_3a60_3ay_3a2002_3ai_3a3_3ap_3a253-263.htm
https://ideas.repec.org/a/eee/stapro/v60y2002i3p253-263.html

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

Tubenet: A Special Trumpetnet for Explicit Solutions to Inverse Problems: TubeNet: a special TrumpetNet for explicit solutions to inverse problems

Authors: Gui-Rong Liu Shuyong Duan Zhang Zhanming et al.

Source: International Journal of Computational Methods. 18:2050030

Subject Terms: 0211 other engineering and technologies, Numerical solution to inverse problems in abstract spaces, 02 engineering and technology, artificial intelligence, 16. Peace & justice, parametric inverse problems, 01 natural sciences, data-driven method, mechanics of composites, Trumpet neural net, deepnets, physic-law-based method, 0101 mathematics, Artificial neural networks and deep learning, TrumpetNet

File Description: application/xml

Access URL: https://zbmath.org/7342029
https://doi.org/10.1142/s0219876220500309
https://www.worldscientific.com/doi/abs/10.1142/S0219876220500309

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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On some inverse problems for distributed parameter systems

Authors: V. I. Agoshkov

Source: Russian Journal of Numerical Analysis and Mathematical Modelling. 18:455-465

Subject Terms: Hilbert spaces, Numerical optimization and variational techniques, convergence, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, numerical algorithms, Numerical solution to inverse problems in abstract spaces, distributed parameter systems, 01 natural sciences, Banach spaces, optimal control, Inverse problems in optimal control, Existence theories for problems in abstract spaces, 0101 mathematics

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Access URL: https://zbmath.org/2051997
https://doi.org/10.1515/156939803322681130
https://www.degruyter.com/view/j/rnam.2003.18.issue-6/156939803322681130/156939803322681130.pdf
http://www.ingentaselect.com/rpsv/cgi-bin/cgi?ini=xref&body=linker&reqdoi=10.1163/156939803322681130

Efficient algorithms for the regularization of dynamic inverse problems: I. Theory: Efficient algorithms for the regularization of dynamic inverse problems. I: Theory

Authors: Alfred K. Louis Uwe Schmitt

Source: Inverse Problems. 18:645-658

Subject Terms: Hilbert spaces, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, dynamic inverse problem, measuring process, static inverse problem, Numerical solution to inverse problems in abstract spaces, Tikhonov Phillips method, 02 engineering and technology, regularizing algorithms, 01 natural sciences, linear operator equations, Numerical solutions to equations with linear operators, projection methods, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Equations and inequalities involving linear operators, with vector unknowns

File Description: application/xml

Access URL: https://zbmath.org/1787294
https://doi.org/10.1088/0266-5611/18/3/308
http://ui.adsabs.harvard.edu/abs/2002InvPr..18..645S/abstract
http://iopscience.iop.org/article/10.1088/0266-5611/18/3/308/pdf