Corpus ID: 237572153

Neural Networks with Inputs Based on Domain of Dependence and A Converging Sequence for Solving Conservation Laws, Part I: 1D Riemann Problems

  title={Neural Networks with Inputs Based on Domain of Dependence and A Converging Sequence for Solving Conservation Laws, Part I: 1D Riemann Problems},
  author={Haoxiang Huang and Yingjie Liu and Vigor Yang},
  • Haoxiang Huang, Yingjie Liu, V. Yang
  • Published 20 September 2021
  • Computer Science, Mathematics, Physics
  • ArXiv
Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear problems, e.g. the Burger’s equation, heat conduction equations, Allen-Cahn and other reaction-diffusion equations, and Navier-Stokes equation. Meanwhile, researchers apply automatic differentiation in physics-informed neural network (PINN) to solve nonlinear… Expand


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