Results 11 to 20 of about 35,012 (233)
Approximation of Bayesian inverse problems for PDEs [PDF]
SIAM Journal on Numerical Analysis, 2009 Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability.
A. M. Stuart +3 more
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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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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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Inverse source problems for degenerate time-fractional PDE [PDF]
Progress in Fractional Differentiation and Applications, 2020 In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one involves a time ...
Al-Salti, Nasser, Karimov, Erkinjon
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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.
Jens Berg, Kaj Nyström
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Bi-level iterative regularization for inverse problems in nonlinear PDEs [PDF]
Inverse Problems, 2023 Abstract We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution partial differential equations (PDEs). We propose a bi-level Landweber scheme, where the upper-level parameter reconstruction embeds a lower-level state approximation.
Tram Thi Ngoc Nguyen
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QEKI: A Quantum–Classical Framework for Efficient Bayesian Inversion of PDEs [PDF]
EntropySolving Bayesian inverse problems efficiently stands as a major bottleneck in scientific computing. Although Bayesian Physics-Informed Neural Networks (B-PINNs) have introduced a robust way to quantify uncertainty, the high-dimensional parameter spaces ...
Jiawei Yong, Sihai Tang
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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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Gaussian Process Regression for Inverse Problems in Linear PDEs
IFAC-PapersOnLineThis paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors defined based on advanced commutative algebra and algebraic analysis. The implementation of these priors is algorithmic
Xin Li +2 more
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