We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of solutions of these dispersive PDEs is leveraged to prove rigorous bounds on the resulting error. We present several numerical experiments to demonstrate that PINNs can approximate solutions of these dispersive PDEs very accurately

翻译：我们建议一种基于物理知情神经网络(PINNs)的新型算法,以高效近似非线性分散式PDE(如KdV-Kawahara、Camassa-Holm和Benjamin-Ono等式)的解决方案。这些分散式PDE的解决方案的稳定性被用来证明由此产生的错误的严格界限。我们提出了一些数字实验,以证明PINNs能够非常准确地接近这些分散式PDE的解决方案。