Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. Th...

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Vydané v:	Journal of scientific computing Ročník 92; číslo 3; s. 88
Hlavní autori:	Cuomo, Salvatore, Di Cola, Vincenzo Schiano, Giampaolo, Fabio, Rozza, Gianluigi, Raissi, Maziar, Piccialli, Francesco
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.09.2022 Springer Nature B.V
Predmet:	Algorithms Applied mathematics Approximation Artificial intelligence Beyond traditional AI: the impact of Machine Learning on Scientific Computing Boundary conditions Computational Mathematics and Numerical Analysis Deep learning Finite element method Literature reviews Machine learning Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Neural networks Partial differential equations Physics Taxonomy Theoretical Nonlinear equations Uncertainty Physics–Informed Neural Networks Numerical methods Deep Neural Networks Scientific Machine Learning Partial Differential Equations
ISSN:	0885-7474, 1573-7691
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Popis
Shrnutí:	Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0885-7474 1573-7691
DOI:	10.1007/s10915-022-01939-z