Analysis of Adaptive Neural Network Methods for Solving the Burger's Equation
This paper describes an adaptive deep learning method for solving partial differential equations.Traditional numerical methods,such as finite element method and finite integral method,suffer from the curse of dimensionality due to the need for mesh partitioning of feasible regions.Methods based on Physics-Informed Neural Networks(PINN)for solving partial differential equations face challenges in terms of accuracy and training efficiency.This paper presents a method called Adaptive Physics-Informed Neural Network(AdaPINN),which combines adaptive activation functions and a loss function weight adaptation strategy.Experimental results demonstrate that AdaPINN exhibits improvements in both the accuracy and training efficiency of solving the Burger equation.
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