Results 21 to 30 of about 1,345 (197)
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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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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Introduction to inverse problems for hyperbolic PDEs
, 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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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.
Cockayne, J +3 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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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 numerical analysis.
Cheng Jin, Liu Jijun, Zhang Bo
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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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