Dosnet as a non-black-box PDE solver: when deep learning meets operator splitting

DOI10.1016/j.jcp.2023.112343arXiv2212.05571MaRDI QIDQ6095076

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Publication date: 27 November 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.05571

zbMATH Keywords

operator splittingSchrödinger equationsneural network architecturedeep learningevolutionary PDEs

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Parabolic equations and parabolic systems (35Kxx) Physiological, cellular and medical topics (92Cxx)

Cites Work

• Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• The phase field method for geometric moving interfaces and their numerical approximations
• Splitting methods
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• Solving high-dimensional partial differential equations using deep learning
• On the Construction and Comparison of Difference Schemes

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