用物理约束神经网络模拟压电材料中电-弹波耦合传播，精度达97%以上。
A Unified Physics-Informed Neural Network for Modeling Coupled Electro- and Elastodynamic Wave Propagation Using Three-Stage Loss Optimization
- 将电-弹动力学方程作为软约束融入神经网络损失函数
- 位移与电势的全局相对L2误差分别低至2.34%和4.87%
- 适合需无网格求解时变耦合偏微分方程的研究者
物理信息神经网络（PINNs）是科学机器学习中一种新方法，通过在损失函数中引入偏微分方程作为软约束，将物理定律直接嵌入神经网络。本文研究了PINNs在求解一维耦合电-弹动力学系统中的应用，该系统以应力-电荷形式建模线性压电效应，由弹性动力学方程和电动力学方程共同控制。采用前馈神经网络架构，输入为时空坐标，输出为机械位移和电势。实验结果表明，该模型对位移和电势的全局相对L2误差分别为2.34%和4.87%，验证了PINNs作为无网格求解器在处理耦合时变偏微分方程系统方面的有效性，但其在耦合特征值系统中仍面临误差累积和刚度问题。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the application of PINNs to solve a one dimensional coupled electro-elastodynamic system modeling linear piezoelectricity in stress-charge form, governed by elastodynamic and electrodynamic equations. Our simulation employs a feedforward architecture, mapping space-time coordinates to mechanical displacement and electric potential. Our PINN model achieved global relative L2 errors of 2.34 and 4.87 percent for displacement and electric potential respectively. The results validate PINNs as effective mesh free solvers for coupled time-dependent PDE systems, though challenges remain regarding error accumulation and stiffness in coupled eigenvalue systems.
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