Concurrent PINN algorithm for solving shallow water wave equations
Hyperbolic conservation equation is a special class of partial differential equations,and the study of its numerical solution method has always been a hot topic.One of its remarkable properties is that its solution may contain discontinuity even if the initial conditions are smooth.As a representation of the nonlinear hyperbolic conservation law,the shallow water wave equation is difficult to be solved precisely because of the existence of discontinuous solutions.In order to solve numerically the shallow water wave equation,a new network is constructed based on the inverse problem framework of PINN(Physics-informed Neural Networks).The network structure consists of two parallel neural networks,one of which is related to the known data obtained by the entropy stable schemes.The other network is related to the equation itself.The unknown water depth is determined by combining the known velocity data with the shallow water wave equation itself.Finally,the feasibility of the network is verified by some numerical examples.The results show that the new network structure can be used to solve the shallow water wave equation,and the water depth can be accurately calculated.
shallow water wave equationdeep learningneural networksshock wave
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维普
