发表机构
Clemson University（克莱姆森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对耦合流体-弹性动力学的热波模型，首次给出了物理信息神经网络（PINN）的误差估计，证明泛化误差受训练误差、求积点数和网络规模控制，并辅以数值实验验证。
AI 中文摘要
我们研究了物理信息神经网络（PINN）对耦合偏微分方程系统的近似，该系统模拟了流体与弹性动力学之间的相互作用。本文所考虑的典型热波模型通过固定边界界面上的传输条件耦合了一个抛物型方程和一个双曲型方程，并作为实际应用中出现的斯托克斯-弹性系统的原型。这种耦合使得误差分析比单一偏微分方程更为精细。我们通过相关的PINN残差来界定精确解与PINN解之间的误差，并且进一步证明了泛化误差受训练误差、求积点数量以及网络规模的控制。据我们所知，这是对耦合流体-结构交互偏微分方程系统的PINN近似的首次误差估计。我们还针对给定的测试问题展示了数值实验。
英文摘要
We study a physics-informed neural network (PINN) approximation of a coupled PDE system that models the interaction between fluid and elastic dynamics. The canonical heat-wave model considered here couples a parabolic and a hyperbolic equation through transmission conditions on a fixed boundary interface, and serves as a prototype for the Stokes-elastic systems that arises in real world applications. This coupling makes the error analysis more delicate than that for a single PDE. We bound the error between the exact and PINN solutions by the associated PINN residuals, and we moreover prove that the generalization error is controlled by the training error, the number of quadrature points, and the size of the network. {To the best of our knowledge}, these are the first error estimates for a PINN approximation of a coupled fluid-structure interaction PDE system. We also show that numerical experiments with respect to a given test problem.
