  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.
