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.

翻译：物理信息神经网络为科学机器学习提供了一种新颖方法，它通过损失函数中的软约束将偏微分方程形式的物理定律直接融入神经网络。本研究探讨了应用PINN求解一维耦合电-弹动力系统的问题，该系统以应力-电荷形式描述线性压电效应，受弹动力方程与电动力方程支配。我们的仿真采用前馈架构，将时空坐标映射为机械位移与电势。所构建的PINN模型在位移和电势预测上分别实现了2.34%和4.87%的全局相对L2误差。研究结果验证了PINN作为耦合时变偏微分方程系统有效无网格求解器的能力，但在耦合特征值系统的误差累积与刚度问题方面仍存在挑战。