Results 31 to 40 of about 2,026 (229)
Variational Autoencoding of PDE Inverse Problems
CoRR, 2020 Specifying a governing physical model in the presence of missing physics and recovering its parameters are two intertwined and fundamental problems in science. Modern machine learning allows one to circumvent these, via emulators and surrogates, but in doing so disregards prior knowledge and physical laws that are especially important for small data ...
Daniel J. Tait, Theodoros Damoulas
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Lift and Relax for PDE-Constrained Inverse Problems in Seismic Imaging [PDF]
IEEE Transactions on Geoscience and Remote Sensing, 2021 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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On inverse problems modeled by PDE’s [PDF]
Matemática Contemporânea, 2000 We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent problems of elliptic, hyperbolic and parabolic types. Each iteration of the analyzed methods consists on the solution of a well posed boundary (or initial) value problem. The
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On some nonlinear fractional PDEs in physics
Bibechana, 2014 In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find
Jamshad Ahmad, Syed Tauseef Mohyud-Din
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Sparse deterministic approximation of Bayesian inverse problems [PDF]
, 2011 We present a parametric deterministic formulation of Bayesian inverse problems with an input parameter from infinite-dimensional, separable Banach spaces.
A M Stuart +5 more
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, 2022 Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique continuation ...
Mishra, Siddhartha, Molinaro, Roberto
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Machine Learning: Science and Technology, 2023 We present novel approximates of variational losses, being applicable for the training of physics-informed neural networks (PINNs). The formulations reflect classic Sobolev space theory for partial differential equations (PDEs) and their weak ...
Juan-Esteban Suarez Cardona +1 more
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Mathematics, 2023 Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws.
Zhixiang Liu +4 more
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Consensus ADMM for Inverse Problems Governed by Multiple PDE Models
CoRR, 2021 The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these large-scale inverse problems into smaller, simpler sub-problems, for which computationally efficient solvers are available ...
Luke Lozenski, Umberto Villa
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Probabilistic numerical methods for PDE-constrained Bayesian inverse problems [PDF]
AIP Conference Proceedings, 2017 This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem.
Jon Cockayne +3 more
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