Results 11 to 20 of about 2,026 (229)
Stochastic Algorithms for Inverse Problems Involving PDEs and many Measurements
SIAM Journal of Scientific Computing, 2014 Inverse problems involving systems of partial differential equations (PDEs) can be very expensive to solve numerically. This is so especially when many experiments, involving different combinations of sources and receivers, are employed in order to ...
Farbod Roosta-Khorasani +2 more
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Approximation of Bayesian inverse problems for PDEs [PDF]
SIAM Journal on Numerical Analysis, 2010 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.
Dashti, Massoumeh +7 more
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Neural networks as smooth priors for inverse problems for PDEs
Journal of Computational Mathematics and Data Science, 2021 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 ...
Jens Berg, Kaj Nyström
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Neural Inverse Operators for Solving PDE Inverse Problems
CoRR, 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.
Mishra, Siddhartha +3 more
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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
doaj +2 more sources
A collage-based approach to solving inverse problems for second-order nonlinear parabolic PDEs
Journal of Mathematical Analysis and Applications, 2013 The essence of collage-based methods for solving inverse problems is to bound the approximation error above by a more readily minimizable distance. The original collage method applies to ordinary differential equations (ODEs) and makes use of Banach's ...
H Kunze, Davide La Torre
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A collage-based approach to solving inverse problems for second-order nonlinear hyperbolic PDEs [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2015 A goal of many inverse problems is to find unknown parameter values, λ ∈ Λ, so that the given observed data utrue agrees well with the solution data produced using these parameters uλ.
H Kunze, Davide La Torre
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Introduction to inverse problems for hyperbolic PDEs
, 2023 There are two main approaches to solve inverse coefficient determination problems for wave equations: the Boundary Control method and an approach based on geometric optics.
Oksanen, Lauri, Nursultanov, Medet
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Bi-level iterative regularization for inverse problems in nonlinear PDEs
Inverse ProblemsWe investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution partial differential equations (PDEs).
Tram Thi Ngoc Nguyen
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Mathematics, 2023 Physics-informed neural networks (PINNs) provide a new approach to solving partial differential equations (PDEs), while the properties of coupled physical laws present potential in surrogate modeling.
Meijun Zhou, Gang Mei, Nengxiong Xu
doaj +1 more source