EPINN: Physics-Informed Neural Network with exponential activation functions for solving stiff ODEs

Yi Zhang, Zhongyi Huang, Ye Li

Keywords: EPINN, stiff ODEs, PINN

Abstract:

Solving stiff ordinary differential equations (ODEs) through machine learning methods has been quite a popular topic for years as it challenges the recently proposed physics-informed neural network (PINN). Many variations based on PINN have been advanced to enhance both the efficiency and the robustness. Nonetheless, many of them need to find the trade-off between the precision and speed because they have to train hundreds or even thousands of parameters if they do not design good or problem-adapt networks. In this scenario, we put forward a single layer physics-informed neural network with exponential activation functions (EPINN) by implementing the prior knowledge of the solution to the linear stiff ODEs. Under this simple but useful structure, less parameters
would be sufficient and the model is easy to train. The model is also extended to solve nonlinear systems by introducing sequential EPINN. The network is tested on six benchmark problems including both linear and nonlinear ones and shows great performance.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 4411