Self-Paced Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations

Xiaoting Han

Abstract: There is a hit discussion on solving partial differential equation by neural network. The famous PINN (physics-informed neural networks) has drawn worldwide attention since it was put forward. Despite its success in solving nonlinear partial differential equation, the difficulty in converging and the inefficiency in training process are definitely huge concerns. Normally, data for PINN is randomly chosen for a given distribution. Additionally, it's fitted to a model in a meaningless way. Curriculum Learning is a learning strategy that trains a model from easy samples to hard ones, which represents the meaningful human learning order. Self-paced Learning (SPL) is one of the significant branches of Automatic Curriculum Learning, which takes example-wise the training loss as Difficulty Measurer. SPL is an efficient strategy in enhancing the convergence rate of numerous models. In this paper, we propose a novel SPL-PINN learning framework, with SPL to accelerate the convergence progress of PINN. We demonstrate the effectiveness of SPL-PINN in a typical parabolic equation and Burgers equation.

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