用神经微分方程融合图网络，提升复杂结构模拟的精度与速度
MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems
- 结合图网络的空间建模与神经微分方程的连续时间演算
- 在大变形非线性问题上预测更准、更稳定，计算速度显著提升
- 适合需要快速高精度仿真的工程结构分析场景
基于网格的物理系统模拟是应用力学的核心，但传统数值求解器在多查询任务中常因计算成本过高而受限。尽管图神经网络（GNN）已成为网格数据的强大代理模型，但其标准自回归方式在长期预测中易出现误差累积与不稳定性。为此，我们提出MeshODENet，一种将GNN空间推理能力与神经微分方程连续时间建模优势相结合的通用框架。我们在一系列具有挑战性的结构力学问题上验证了该框架的有效性与泛化能力，涵盖一维与二维弹性体在大尺度非线性变形下的行为模拟。结果表明，该方法在长期预测精度和稳定性方面显著优于基线模型，同时相比传统求解器实现显著的计算加速。本工作为开发数据驱动的高效代理模型以加速复杂结构系统的分析与建模提供了强有力且可推广的方法。
原文摘要 · Abstract (English)
The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have emerged as powerful surrogate models for mesh-based data, their standard autoregressive application for long-term prediction is often plagued by error accumulation and instability. To address this, we introduce MeshODENet, a general framework that synergizes the spatial reasoning of GNNs with the continuous-time modeling of Neural Ordinary Differential Equations. We demonstrate the framework's effectiveness and versatility on a series of challenging structural mechanics problems, including one- and two-dimensional elastic bodies undergoing large, non-linear deformations. The results demonstrate that our approach significantly outperforms baseline models in long-term predictive accuracy and stability, while achieving substantial computational speed-ups over traditional solvers. This work presents a powerful and generalizable approach for developing data-driven surrogates to accelerate the analysis and modeling of complex structural systems.
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