arXiv:2505.07090cs.LG2025-05被引 7

用物理约束的多输入网络,秒级预测结构动态响应。

Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures

  • 引入双主干网络显式建模时间动态,实现时空连续预测。
  • 在梁和KW-51桥上达到FEM精度,推理速度超GRU-DeepONet 100倍。
  • 适合实时结构监测与数字孪生,无需求解偏微分方程。

有限元(FE)建模对结构分析至关重要,但在动态载荷下仍计算成本高昂。尽管操作学习模型已在静态响应预测中达到FEM级精度,但动态行为建模仍具挑战。本文提出多输入操作网络(MIONet),通过引入第二主干网络显式编码时间动态,实现对移动荷载下结构响应的精确连续预测。传统基于循环神经网络(RNN)的DeepONet受限于固定时间离散化,难以捕捉连续动力学。相比之下,MIONet可连续预测时空全域响应,无需分步建模。它将荷载类型、速度、空间网格及时间步数等标量输入映射为全域结构响应。为提升效率并保证物理一致性,采用基于预计算质量、阻尼和刚度矩阵的物理信息损失函数,无需直接求解控制偏微分方程。此外,利用舒尔补公式缩小训练域,显著降低计算开销同时保持全局精度。模型在简支梁和KW-51桥上验证,实现秒级内达到FEM级精度。相比基于GRU的DeepONet,本模型具备相当精度、更优时间连续性,且推理速度提升超过100倍,适用于实时结构监测与数字孪生应用。

原文摘要 · Abstract (English)

Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM level accuracy, modeling dynamic behavior remains more challenging. This work presents a Multiple Input Operator Network (MIONet) that incorporates a second trunk network to explicitly encode temporal dynamics, enabling accurate prediction of structural responses under moving loads. Traditional DeepONet architectures using recurrent neural networks (RNNs) are limited by fixed time discretization and struggle to capture continuous dynamics. In contrast, MIONet predicts responses continuously over both space and time, removing the need for step wise modeling. It maps scalar inputs including load type, velocity, spatial mesh, and time steps to full field structural responses. To improve efficiency and enforce physical consistency, we introduce a physics informed loss based on dynamic equilibrium using precomputed mass, damping, and stiffness matrices, without solving the governing PDEs directly. Further, a Schur complement formulation reduces the training domain, significantly cutting computational costs while preserving global accuracy. The model is validated on both a simple beam and the KW-51 bridge, achieving FEM level accuracy within seconds. Compared to GRU based DeepONet, our model offers comparable accuracy with improved temporal continuity and over 100 times faster inference, making it well suited for real-time structural monitoring and digital twin applications.

结构预测物理信息网络动态响应数字孪生

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