EM-RBN:一种基于融合网络和动态权重生成的物理信息神经网络算法

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

  • 摘要: 物理信息神经网络算法通过融合深度学习和物理定律,为偏微分方程智能代理求解提供了有效解决方案。针对传统物理信息神经网络因频谱偏差问题导致的收敛效率低、预测精度差等问题,本文提出一种基于融合网络和动态权重生成的物理信息神经网络算法(EM-RBN),该算法通过设计基于数据增强变换的多层感知机和径向基融合子网络,高效捕捉跨频率特征。同时,在网络中引入动态权重生成模块,实时学习并调整子网络输出权重以平衡高低频特征的贡献。实验结果表明,EM-RBN方法在不同数值问题上相较于已有物理信息神经网络算法最高实现了两个数量级的预测精度提升。本文的代码开源在https: //github.com/jia-chen25/EM-RBN。

     

    Abstract: Physics-informed neural network algorithms provide an effective solution for surrogate solving of partial differential equations by integrating deep learning with physical laws. Because of the low convergence efficiency and prediction accuracy of clasical physics-informed neural network caused by spectral bias, a physics-informed neural network algorithm (EM-RBN) based on integrated networks and dynamic weight generation was proposed. This algorithm captures cross-frequency features by designing a multi-layer perceptron based on data augmentation transformation and a radial basis sub network. Additionally, a dynamic weight generation module is introduced to learn and adjust the output weights of sub-networks in real time, thereby balancing the contributions of high and low frequency features. Experimental results show that the EM-RBN method achieves a maximum prediction accuracy improvement of two orders of magnitude compared with existing physics-informed neural network algorithms across different numerical problems. The code of this paper is open-sourced at https: //github.com/jia-chen25/EM-RBN.

     

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