基于物理信息神经网络求解偏微分方程
Solving Partial Differential Equations Based on Physics-Informed Neural Networks
摘要: 本文聚焦偏微分方程的求解问题。应用物理信息神经网络(Physics-Infor-med Neural Networks, PINN-s)，将传统偏微分方程求解问题转化为神经网络的优化训练过程。通过将物理定律以软约束形式嵌入神经网络架构，构建了一种偏微分方程快速求解器。数值实验表明，该方法在有限数据条件下即可实现方程未知参数的高精度反演，并能构建出具有较高精度的预测解。
Abstract: This study focuses on the efficient solution of partial differential equations by applying Physics-Informed Neural Networks (PINNs). The method transforms the traditional PDE solving problem into an optimization training process of neural networks. By embedding physical laws as soft constraints into the neural network architecture, a novel fast solver for PDEs is constructed. Numerical experiments demonstrate that this approach can achieve high-precision inversion of unknown parameters in equations and construct predictive solutions with high accuracy, even under limited data conditions.
文章引用：贾兴卓. 基于物理信息神经网络求解偏微分方程[J]. 统计学与应用, 2025, 14(3): 249-256. https://doi.org/10.12677/sa.2025.143076

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