Solution approach of Burgers-Fisher equation based on physics-informed neural networks

Physical information was divided into rule information and numerical information, in order to explore the role of physical information in training neural network when solving differential equations with physics-informed neural network (PINN). The logic of PINN for solving differential equations was explained, as well as the data-driven approach of physical information and neural network interpretability. Synthetic loss function of neural network was designed based on the two types of information, and the training balance degree was established from the aspects of training sampling and training intensity. The experiment of solving the Burgers-Fisher equation by PINN showed that PINN can obtain good solution accuracy and stability. In the training of neural networks for solving the equation, numerical information of the Burgers-Fisher equation can better promote neural network to approximate the equation solution than rule information. The training effect of neural network was improved with the increase of training sampling, training epoch, and the balance between the two types of information. In addition, the solving accuracy of the equation was improved with the increasing of the scale of neural network, but the training time of each epoch was also increased. In a fixed training time, it is not true that the larger scale of the neural network, the better the effect. © 2023 Zhejiang University. All rights reserved.