It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.

中文翻译：

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一种求解三阶非线性发展方程的深度学习方法

仍然难以解析地解决非线性发展方程。在本文中，我们提出了一种直接从时空数据中恢复固有非线性动力学的深度学习方法。具体而言，该模型使用受给定控制方程约束的深度神经网络来尝试学习所有最佳参数。特别是，对几个三阶非线性发展方程，包括Korteweg-de Vries（KdV）方程，修正的KdV方程，KdV-Burgers方程和Sharma-Tasso-Olver方程的数值实验表明，该方法能够发现孤子及其交互行为相当好。