wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws
DOI10.1137/22m1522504arXiv2207.08483OpenAlexW4392817028MaRDI QIDQ6197777
Tim De Ryck, Roberto Molinaro, Siddhartha Mishra
Publication date: 20 March 2024
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2207.08483
Artificial neural networks and deep learning (68T07) Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Shock waves and blast waves in fluid mechanics (76L05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Inverse problems for PDEs (35R30) Existence of solutions for minimax problems (49J35) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Weak solutions to PDEs (35D30) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Blow-up in context of PDEs (35B44)
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