In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms.

翻译：本文提出了一种非扩散神经网络（NDNN）算法，用于精确求解双曲守恒律的弱解。其原理是通过在由间断线（DLs）界定的子域中计算光滑局部解来构造这些弱解，其中间断线由Rankine-Hugoniot跳跃条件定义。所提出的方法能够有效处理任意数量的熵激波、激波生成以及波相互作用问题。文中通过数值实验展示了该算法的优势与特性。