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Improve the discontinuity capturing ability of physics-informed neural network
  • Li Liu


In this paper, we proposed a method to improve the discontinuities (especially shock waves) capturing ability of physics-informed-neural-networks (PINN) in simulating hyperbolic equations. The main idea of the method is to weaken the influence of the points inside discontinuities which can not be expressed directly by the differential equations theoretically, and may let the trainings fall into a confrontation with the physics compressible effect. In this work, we add a weight to each point which is related to the gradient locally, then the network can focus on training the ‘differential equations expressed points’(smooth points). Automatically by the physical compressible effect, all the nearby points will move out of the discontinuously regions, and gain a sharp and exact result automatically with the physical process inside the training