Data-driven Discovery of Modified Kortewegde Vries Equation, Kdv-Burger Equation and Huxley Equation by Deep Learning

In this paper, with the aid of symbolic computation system Python, and based on the Deep Neural Network, Automatic differentiation and Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization algorithms, the model parameters of modified Kortewegde Vries (mkdv) equation Kdv-Burger equation and Huxley equation are obtained. We added different amounts of noise to the clean data in experiment and found that with the addition of trace noise, the parameters of the differential equation can also be accurately found. The result indicates that the algorithm has little effect on trace noise and shows better robustness to data noise. The method in this paper has demonstrated the powerful mathematical and physical ability of deep learning to flexibly simulate the physical dynamic state represented by differential equations, which opens the way for us to understand more physical phenomena later and the algorithm may be suitable for the data in practical application.