2024/04/01 by Nan Zhou, Zheng Ma, Zhou, Nan +1 · 2 citations
Computer Science · Engineering · #35D99 #65D15 #68T07 #76L05 #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Seismology and Earthquake Studies #Traffic Prediction and Management Techniques
paper · pdf · doi:10.48550/arxiv.2404.01163
openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we put forward a neural network framework to solve the nonlinear hyperbolic systems. This framework, named relaxation neural networks(RelaxNN), is a simple and scalable extension of physics-informed neural networks(PINN). It is shown later that a typical PINN framework struggles to handle shock waves that arise in hyperbolic systems' solutions. This ultimately results in the failure of optimization that is based on gradient descent in the training process. Relaxation systems provide a smooth asymptotic to the discontinuity solution, under the expectation that macroscopic problems can be solved from a microscopic perspective. Based on relaxation systems, the RelaxNN framework alleviates the conflict of losses in the training process of the PINN framework. In addition to the remarkable results demonstrated in numerical simulations, most of the acceleration techniques and improvement strategies aimed at the standard PINN framework can also be applied to the RelaxNN framework.