Yiwen Pang
ABSTRACT
Physics-informed neural networks (PINNs) have recently been demonstrated to be effective for the numerical solution of differential equations, with the advantage of small real labelled data needed. However, the performance of PINN greatly depends on the differential equation. The solution of singularly perturbed differential equations (SPDEs) usually contains a boundary layer, which makes it difficult for PINN to approximate the solution of SPDEs. In this paper, we analyse the reasons for the failure of PINN in solving SPDE and provide a feasible solution by adding prior knowledge of the boundary layer to the neural network. The new method is called the tailored physics-informed neural network (TPINN) since the network is tailored to some particular properties of the problem. Numerical experiments show that our method can effectively improve both the training speed and accuracy of neural networks.
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Index Terms
- A Tailored Physics-informed Neural Network Method for Solving Singularly Perturbed Differential Equations
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