EM-RBN: A Physics-Informed Neural Network Algorithm Based on Integrated Networks and Dynamic Weight Generation

This branch contains the code for paper: EM-RBN: A Physics-Informed Neural Network Algorithm Based on Integrated Networks and Dynamic Weight Generation

融合网络架构

动态权重生成模块

Usage

The usage instructions for this branch are consistent with those in the main branch. Please refer to the main branch documentation for detailed setup and execution guidelines.

Benchmarks

The following table shows the performance of EM-RBN compared to Vanilla PINN and PIRBN on a set of benchmark problems. The accuracy is measured in relative $L^{2}$ error between the predicted and true solutions.

Benchmark	EM-RBN	PIRBN	Vanilla PINN
Helmholtz2D($\alpha_{1}=1,\alpha_{2}=8$)	$7.45×10^{-3}$	$6.81×10^{-2}$	$1.51$
Helmholtz2D($\alpha_{1}=6,\alpha_{2}=6$)	$6.60×10^{-3}$	$1.05×10^{-2}$	$1.78$
Helmholtz2D($\alpha_{1}=1,\alpha_{2}=4$)	$9.97×10^{-3}$	$3.75×10^{-2}$	$9.59×10^{-2}$
Helmholtz2D($\alpha_{1}=2,\alpha_{2}=3$)	$9.71×10^{-3}$	$3.90×10^{-2}$	$7.98×10^{-2}$
Wave2D	$7.02×10^{-2}$	$2.09×10^{-1}$	$4.90×10^{-1}$
Klein–Gordon1D	$4.68×10^{-2}$	$9.18×10^{-2}$	$7.04×10^{-1}$
Navier-Stokes	$2.06×10^{-2}$	$7.02×10^{-2}$	$1.21×10^{-1}$