论文标题
设计神经网络用于双曲线保护法
Designing Neural Networks for Hyperbolic Conservation Laws
论文作者
论文摘要
我们提出了一种新的数据驱动方法，以了解使用深神经网络的未知双曲线保护法的动态。受数值保护法中经典方法的启发，我们开发了一个新的保守形式网络（CFN），其中网络在其中学习未知系统的通量功能。我们的数值示例表明，即使使用标准的非保守形式网络获得的CFN比使用标准非保守形式网络获得的预测准确性明显更好，即使它受到限制以促进保护。特别是，使用CFN获得的溶液始终捕获正确的冲击传播速度，而无需将非物理振荡引入溶液中。他们对嘈杂且稀疏的观察环境也很强。
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 enhanced with constraints to promote conservation. In particular, solutions obtained using the CFN consistently capture the correct shock propagation speed without introducing non-physical oscillations into the solution. They are furthermore robust to noisy and sparse observation environments.
