Physics-informed neural networks for 2nd order ODEs with sharp gradients

DOI10.1016/j.cam.2023.115396OpenAlexW4380874473MaRDI QIDQ6049309

Francesco Calabrò, Roberto Furfaro, Enrico Schiassi, Mario De Florio

Publication date: 15 September 2023

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2023.115396

zbMATH Keywords

least-squaresextreme learning machinephysics-informed neural networksfunctional interpolation

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Cites Work

• The theory of connections: connecting points
• Physics-informed neural networks for rarefied-gas dynamics: Poiseuille flow in the BGK approximation
• Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines
• Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
• Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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