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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.
Simon L. Cotter +2 more
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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
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Қарағанды университетінің хабаршысы. Математика сериясы, 2022 Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity.
M.J. Huntul, I. Tekin
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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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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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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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Model Reduction and Neural Networks for Parametric PDEs [PDF]
, 2020 We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model ...
Bhattacharya, Kaushik +3 more
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