文章详情

摘要

针对物理信息神经网络（Physics-Informed Neural Network, PINN）求解微分方程精度受限的问题，提出一种多隐藏层综合输出的readout-PINN架构，通过融合各隐藏层输出得到最终解。以一维、二维泊松方程为算例，采用有限记忆BFGS（L-BFGS）优化训练，并与同规模PINN、梯度增强物理PINN（Gradient-enhanced PINN, gPINN）及hp-变分PINN（hp-Variational PINN, hp-VPINN）对比。结果表明：相较PINN，一维最大绝对误差与均方误差降低93.1%与99.1%；二维降低72.6%与93.6%，在保持高精度的同时计算开销低于gPINN与hp-VPINN。

关键词

泊松方程；物理信息神经网络；神经网络架构；高频微分方程

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作者简介

林于暄（1999—），女，汉族，河南商丘人，硕士研究生在读，研究方向：神经网络解微分方程。