Computational issues based on neural networks for a class of systems of conservation laws

The aim of the present paper is to numerically solve a class of systems of conservation laws, modeled by hyperbolic partial differential equations (hPDEs). Our approach considers a novel computational procedure which relies on using the repetitive structure induced by a convergent Method of Lines for assigning a cell-based recurrent neural network to perform the numerics. Emphasizing that the Method of Lines is more a concept than a specific procedure, our approach ensures the convergence of the approximation and preserves the basic properties of the solution of the initial hPDE problem, i.e. existence, uniqueness, data dependence and stability in the sense of Lyapunov. The procedure is applied on a bilinear control system arising from the process of combined heat-electricity generation. Simulation results are provided.