Higher-order error estimates for physics-informed neural networks approximating the primitive equations

DOI10.1007/s42985-023-00254-yzbMath1529.35517arXiv2209.11929OpenAlexW4384825978MaRDI QIDQ6114171

Alan Raydan, Ruimeng Hu, Quyuan Lin, S. Tang

Publication date: 14 August 2023

Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.11929

zbMATH Keywords

numerical analysisprimitive equationshydrostatic Navier-Stokes equationsphysics-informed neural networkshigher-order error estimates

Mathematics Subject Classification ID

Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) A priori estimates in context of PDEs (35B45) Theoretical approximation in context of PDEs (35A35) Meteorology and atmospheric physics (86A10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Geophysical flows (76U60)

Related Items (1)

Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms

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