In this paper, with the aid of symbolic computation system Python and based on the deep neural network (DNN), automatic differentiation (AD), and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization algorithms, we discussed the modified Korteweg-de Vries (mkdv) equation to obtain numerical solutions. From the predicted solution and the expected solution, the resulting prediction error reaches . The method that we used in this paper had demonstrated the powerful mathematical and physical ability of deep learning to flexibly simulate the physical dynamic state represented by differential equations and also opens the way for us to understand more physical phenomena later.

中文翻译：

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深度学习启发物理学：修正 Korteweg-de Vries 方程的数值解

在本文中，借助符号计算系统 Python 并基于深度神经网络 (DNN)、自动微分 (AD) 和有限内存的 Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) 优化算法，我们讨论了修正 Korteweg-de Vries (mkdv) 方程以获得数值解。从预测解和期望解来看，得到的预测误差达到。我们在本文中使用的方法展示了深度学习强大的数学和物理能力，可以灵活地模拟微分方程表示的物理动态，也为我们以后理解更多物理现象开辟了道路。