Designing Neural Networks for Hyperbolic Conservation Laws

@article{Chen2022DesigningNN,
  title={Designing Neural Networks for Hyperbolic Conservation Laws},
  author={Zhen Chen and Anne Gelb and Yoonsang Lee},
  journal={ArXiv},
  year={2022},
  volume={abs/2211.14375}
}
We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form network (CFN) in which the network learns the flux function of the unknown system. Our numerical examples demonstrate that the CFN yields significantly better prediction accuracy than what is obtained using a standard non-conservative form network, even when it is… 
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