Understand
The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous solutions.
- In this paper, we focus on the discrete time physics-informed neural network (PINN), and propose a hybrid PINN scheme for the nonlinear PDEs.
- In this approach, the local solution structures are classified as smooth and nonsmooth scales by introducing a discontinuity indicator, and then the automatic differentiation technique is employed for resolving smooth scales, while an improved weighted essentially non-oscillatory (WENO) scheme is adopted to capture discontinuities.
- We then test the present approach by considering the viscous and inviscid Burgers equations , and it is shown that compared with original discrete time PINN, the present hybrid approach has a better performance in approximating the discontinuous solution even at a relatively larger time step.