Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next
2022/01/14 by Salvatore Cuomo, Cuomo, Salvatore, Vincenzo Schiano di Cola +10 · 219 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Collocation (remote sensing) #Computer science #Engineering #Finite element method #Function (biology) #Machine learning #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Partial differential equation #Physics #Range (aeronautics) #cs.AI #cs.LG #cs.NA #math.NA #physics.data-an
paper · pdf · doi:10.48550/arxiv.2201.05624
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/01/14 · openalex created_date 2022/04/03 · arxiv created 2022/06/07 · arxiv updated 2022/06/08 · openalex updated_date 2026/08/06
Abstract
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.
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