HT-PeRCNN:基于Hessian矩阵迹权重的物理编码递归卷积神经网络OA
HT-PeRCNN:Physics-encoded Recurrent Convolutional Neural Network Based on Hessian Trace Weight
近年来,物理信息神经网络作为一种基于深度学习的偏微分方程求解方法,在多个领域取得了显著进展.然而,物理信息神经网络仍然存在训练效率低以及推理速度慢等问题.针对这些问题,该研究提出了一种基于Hessian矩阵迹权重的物理编码递归卷积神经网络(Physics-encoded Recurrent Convolutional Neural Network,PeRCNN)改进方法,HT-PeRCNN.该方法利用Hessian矩阵迹作为权重调节因子,以优化损失函数的权重分配,提高了模型的稳定性和外推能力.实验结果表明,与PeRCNN相比,HT-PeRCNN在多个PDE求解任务中将方程解的精度提高了50%.
In recent years,Physics-Informed Neural Networks(PINNs)have achieved significant progress as a Deep Learning-based approach for solving Partial Differential Equations(PDEs)in various fields.However,PINNs still suffer from problems of low training efficiency and slow inference speed.To address these problems,this study proposes an improved method of Physics-encoded Recurrent Convolutional Neural Network(PeRCNN)based on the Hessian trace weight,named HT-PeRCNN.The method uses the Hessian trace as a weighted factor to optimize the weighted distribution of loss function,enhancing model stability and extrapolation capability.Experimental results show that HT-PeRCNN improves solution accuracy by 50%compared to PeRCNN in multiple PDE-solving tasks.
伏倩
中国石油化工股份有限公司胜利油田分公司滨南采油厂 信息化服务中心,山东 滨州 256600
计算机与自动化
偏微分方程物理信息神经网络物理编码递归卷积神经网络Hessian矩阵迹权重
PDEPINNPeRCNNHessian trace weight
《现代信息科技》 2025 (11)
25-32,37,9
评论