Results 11 to 20 of about 35,710 (245)
Neural Inverse Operators for Solving PDE Inverse Problems [PDF]
International Conference on Machine Learning, 2023 A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data.
R. Molinaro +3 more
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Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems [PDF]
arXiv.orgInverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach.
Sung Woong Cho, Hwijae Son
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Inverse problems for PDEs: Models, computations and applications [PDF]
SCIENTIA SINICA Mathematica, 2018 Inverse problems for partial differential equations (PDEs) are of great importance in the areas of applied mathematics, whichcover different mathematical branches including PDEs, functional analysis, nonlinear analysis,optimizations, regularization and ...
Cheng Jin, L. Jijun, Zhang Bo
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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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Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs [PDF]
SIAM Journal on Scientific Computing, 2020 Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as well as Markov ...
Ilona Ambartsumyan +7 more
semanticscholar +6 more sources
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
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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).
B. Harrach
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Latent Neural Operator for Solving Forward and Inverse PDE Problems [PDF]
Neural Information Processing SystemsNeural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values.
Wang Tian, Chuang Wang
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Lift and Relax for PDE-Constrained Inverse Problems in Seismic Imaging [PDF]
IEEE Transactions on Geoscience and Remote Sensing, 2020 We present Lift and Relax for Waveform Inversion (LRWI), an approach that mitigates the local minima issue in seismic full waveform inversion (FWI) via a combination of two convexification techniques. The first technique (Lift) extends the set of variables in the optimization problem to products of those variables, arranged as a moment matrix.
Zhilong Fang, Laurent Demanet
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Inverse problems for semilinear elliptic PDE with measurements at a single point
Proceedings of the American Mathematical Society, 2023 We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the Dirichlet-to-Neumann map measured at a single boundary point, or integrated against a fixed measure. This result is valid
Mikko Salo, Leo Tzou
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