On stability and regularization for data-driven solution of parabolic inverse source problems (Q2112451)

scientific article; zbMATH DE number 7640536

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English	On stability and regularization for data-driven solution of parabolic inverse source problems	scientific article; zbMATH DE number 7640536

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instance of

scholarly article

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title

On stability and regularization for data-driven solution of parabolic inverse source problems (English)

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Journal of Computational Physics

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publication date

11 January 2023

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zbMATH Keywords

data-driven

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deep neural networks

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inverse source problem

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generalization error estimates

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numerics

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describes a project that uses

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full work available at URL

https://doi.org/10.1016/j.jcp.2022.111769

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cites work

Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I

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Numerical solution of inverse problems by weak adversarial networks

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Reconstruction of a spacewise-dependent heat source in a time-dependent heat diffusion process

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Q5189317

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Solving high-dimensional partial differential equations using deep learning

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Determination of a term in the right-hand side of parabolic equations

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An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

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Multilayer feedforward networks are universal approximators

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Inverse problems for partial differential equations

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

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Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems

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Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

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A variational method for identifying a spacewise-dependent heat source

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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Physics-informed neural networks for high-speed flows

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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On the stable numerical evaluation of Caputo fractional derivatives

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Determination of a time-dependent term in the right-hand side of linear parabolic equations

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ON CERTAIN INVERSE PROBLEMS FOR PARABOLIC EQUATIONS WITH FINAL AND INTEGRAL OBSERVATION

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Inverse source problem for parabolic equation with the condition of integral observation in time

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Q4256419

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Inverse heat source problem from time distributing overdetermination

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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

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DGM: a deep learning algorithm for solving partial differential equations

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Weak adversarial networks for high-dimensional partial differential equations

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2022.111769

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Mathematics(1 entry)

mardi Publication:2112451