A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions (Q6048429)

scientific article; zbMATH DE number 7748050

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English	A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions	scientific article; zbMATH DE number 7748050

Statements

instance of

scholarly article

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title

A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions (English)

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George Em. Karniadakis

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Robert M. Kirby

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published in

Journal of Computational Physics

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publication date

10 October 2023

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full work available at URL

https://arxiv.org/abs/2302.14227

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zbMATH Keywords

physics-informed neural networks (PINNs)

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causality

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domain decomposition

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transfer learning

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MaRDI profile type

MaRDI publication profile

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cites work

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

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Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

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Deep learning of free boundary and Stefan problems

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Scientific machine learning through physics-informed neural networks: where we are and what's next

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Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

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When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

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Kolmogorov n-width and Lagrangian physics-informed neural networks: a causality-conforming manifold for convection-dominated PDEs

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Physics-informed neural networks for inverse problems in supersonic 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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DeepXDE: A Deep Learning Library for Solving Differential Equations

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

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Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

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

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PPINN: parareal physics-informed neural network for time-dependent PDEs

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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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Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

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On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks

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A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations

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A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

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When and why PINNs fail to train: a neural tangent kernel perspective

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Q5270493

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On the limited memory BFGS method for large scale optimization

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Physics-informed neural networks for the shallow-water equations on the sphere

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Parallel physics-informed neural networks via domain decomposition

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Exponential time differencing for stiff systems

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Identifiers

arXiv ID

2302.14227

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DOI

10.1016/j.jcp.2023.112464

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6048429