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Neural Inverse Operators for solving PDE Inverse Problems
, 2023 Data and models for the paper "Neural Inverse Operators for solving PDE Inverse Problems"
Anonymous
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An Introduction to Finite Element Methods for Inverse Coefficient Problems in Elliptic PDEs [PDF]
Jahresbericht Der Deutschen Mathematiker-vereinigung, 2021 Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s).
Bastian Harrach
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Introduction to inverse problems for hyperbolic PDEs [PDF]
, 2023 These lecture notes were written for CIRM SMF School Spectral Theory, Control and Inverse Problems, November ...
Medet Nursultanov, Lauri Oksanen
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A penalty method for PDE-constrained optimization in inverse problems [PDF]
Inverse Problems, 2015 Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-
Herrmann, Felix J., van Leeuwen, Tristan
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Neural networks as smooth priors for inverse problems for PDEs
Journal of Computational Mathematics and Data Science, 2021 Abstract In this paper we discuss the potential of using artificial neural networks as smooth priors in classical methods for inverse problems for PDEs. Exploring that neural networks are global and smooth function approximators, the idea is that neural networks could act as attractive priors for the coefficients to be estimated from noisy data.
J. Berg, K. Nyström
semanticscholar +3 more sources
The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses
Examples and CounterexamplesThis paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation.
Yohan Chandrasukmana +2 more
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Wasit Journal of Computer and Mathematics ScienceThis paper addresses the inverse problem of reconstructing complete steady-state solutions for elliptic partial differential equations when boundary information is incomplete a situation common in electromagnetic, thermal, and geophysical modeling where ...
ABBAS ALDNADOI
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Inverse Source Problems for Degenerate Time-Fractional PDE [PDF]
Progress in Fractional Differentiation and Applications, 2022 12 pages, 8 ...
Al-Salti, Nasser, Karimov, Erkinjon
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Graph Neural Regularizers for PDE Inverse Problems [PDF]
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme that alternates between FEM-based inversion and learned graph neural regularization.
William Lauga +5 more
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Structured Random Sketching for PDE Inverse Problems [PDF]
SIAM Journal on Matrix Analysis and Applications, 2020 For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with $\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x \, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable solution $\mathsf{x}$.
Ke Chen +3 more
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