Results 11 to 20 of about 2,057 (240)
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. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of
S. L. Cotter +2 more
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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 ...
Nursultanov, Medet, Oksanen, Lauri
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Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs [PDF]
, 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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A deep neural network approach for parameterized PDEs and Bayesian inverse problems
Machine Learning: Science and Technology, 2023 We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems.
Harbir Antil +3 more
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An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics. [PDF]
PLoS ONE, 2014 In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is ...
Jamshad Ahmad, Syed Tauseef Mohyud-Din
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DISCRETE NON-STANDARD FORMULATION OF PDE INVERSE PROBLEMS
International Journal of Numerical Methods and Applications, 2022 Abstract In this paper, we are interested in the computation of the unknown initial state for the simulation and prediction of PDE systems where the solution measures are partially known over a time interval. Such a problem is usually solved by an ill-posed optimal control problem.
Cyr S. Ngamouyih Moussata +3 more
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Applied Sciences, 2023 Numerical methods, such as finite element or finite difference, have been widely used in the past decades for modeling solid mechanics problems by solving partial differential equations (PDEs).
Yawen Deng +5 more
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On an inverse problem for a nonlinear third order in time partial differential equation
Results in Applied Mathematics, 2022 In this article, first we convert an inverse problem of determining the unknown timewise terms of nonlinear third order in time partial differential equation (PDE) from knowledge of two boundary measurements to the auxiliary system of integral equations.
M.J. Huntul, I. Tekin
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FDM data driven U-Net as a 2D Laplace PINN solver
Scientific Reports, 2023 Efficient solution of partial differential equations (PDEs) of physical laws is of interest for manifold applications in computer science and image analysis. However, conventional domain discretization techniques for numerical solving PDEs such as Finite
Anto Nivin Maria Antony +2 more
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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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