Application of region compression PINN algorithm in solving hyperbolic conservation laws
In order to capture the discontinuities and improve the accuracy of the algorithm,the region compression PINN algorithm is used to approximate the hyperbolic conservation laws.First of all,the velocity gradient monitoring function is added to the physical equation to identify and compress the large gradient region.Then,for hyperbolic conservation laws with different initial conditions,the corresponding compression control coefficient of the large gradient region is set to reduce its proportion in the loss function.Finally,the loss function with the velocity gradient weight term is put into the neural network for training,and through learning the solution of the equation over the entire region is obtained by minimizing the loss function.This paper applies this algorithm to various classical cases,by numerical simulation of one-dimensional and two-dimensional hyperbolic conservation laws satisfying different initial conditions.Compared with the results of classical PINN algorithm,the good performance of this algorithm is verified.
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