Simulating partial differential equations with neural networks

DOI10.1007/978-3-031-55264-9_4MaRDI QIDQ6613539

Christopher Leonard, Alina Chertock

Publication date: 2 October 2024

zbMATH Keywords

neural networkspartial differential equationsfinite-volume methods

Mathematics Subject Classification ID

Numerical analysis (65-XX) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Cites Work

• Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
• Multilayer feedforward networks are universal approximators
• Deep neural network modeling of unknown partial differential equations in nodal space
• Data driven governing equations approximation using deep neural networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Strong stability-preserving high-order time discretization methods
• Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations

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