A numerical method to solve PDE through PINN based on ODENet

Abstract

With the rapid development of articial intelligence, especially deep learning technology, scientic researchers have begun to explore its application in the eld of traditional scientic computing. Traditional scientic computing relies on mathematical equations to describe and predict the scientic laws of nature, while deep learning provides a new perspective to solve complex mathematical problems by learning patterns in data. The introduction of the Physical Information Neural Network (PINN) and the Ordinary Dierential Equation (ODENet) network layer enables deep learning technology to more accurately simulate and predict scientic phenomena. This study shows that by embedding an ODE-Net network layer in a physical information neural network (PINN), the tting accuracy and generalization performance of the model can be signicantly improved. Experimental results show that compared with traditional numerical methods and fully connected neural networks, this model combined with deep learning technology not only shows higher accuracy when solving partial dierential equations, but also exhibits faster convergence speed and stronger adaptability. These ndings not only promote the integration of scientic computing and deep learning, but also provide new research directions and practical strategies for using deep learning technology to solve complex scientic problems.