arXiv:2604.07746cs.LGcs.CE2026-04被引 4

用多源数据快速发现可解释的材料本构模型,提升有限元仿真效率。

Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)

  • 结合物理约束与稀疏化,从多模态数据中自动发现简洁本构模型。
  • 仅需少量测试数据和全场变形信息,即可实现快速建模与模型更新。
  • 适合需要快速迭代仿真、追求可解释性的工程材料研发人员。

近年来,基于AI的本构建模研究正从纯数据驱动转向引入物理约束与机制原理,即物理增强。传统现象学方法依赖预设模型并校准参数,而机器学习方法则侧重模型本身发现。稀疏回归介于两者之间,在校准过程中从大量预定义模型库中筛选最优项。稀疏化不仅提升模型可解释性与不确定性量化能力,也因低维特性利于异构软件集成。现有研究多集中于单一数据源,但实际材料建模常包含多源数据(多模态)及同类别材料间的跨材料数据(多保真度)。本文提出物理增强有限元模型更新(paFEMU),一种迁移学习框架,融合AI本构建模、稀疏化以实现可解释模型发现,以及基于有限元的伴随优化,利用简单力学测试数据(可能来自不同材料)与数字图像相关法全场数据,实现快速本构模型发现。稀疏表示的简洁性使其易于嵌入现有有限元流程,并支持迁移学习中的低维更新。

原文摘要 · Abstract (English)

Recent progress in AI-enabled constitutive modeling has concentrated on moving from a purely data-driven paradigm to the enforcement of physical constraints and mechanistic principles, a concept referred to as physics augmentation. Classical phenomenological approaches rely on selecting a pre-defined model and calibrating its parameters, while machine learning methods often focus on discovery of the model itself. Sparse regression approaches lie in between, where large libraries of pre-defined models are probed during calibration. Sparsification in the aforementioned paradigm, but also in the context of neural network architecture, has been shown to enable interpretability, uncertainty quantification, but also heterogeneous software integration due to the low-dimensional nature of the resulting models. Most works in AI-enabled constitutive modeling have also focused on data from a single source, but in reality, materials modeling workflows can contain data from many different sources (multi-modal data), and also from testing other materials within the same materials class (multi-fidelity data). In this work, we introduce physics augmented finite element model updating (paFEMU), as a transfer learning approach that combines AI-enabled constitutive modeling, sparsification for interpretable model discovery, and finite element-based adjoint optimization utilizing multi-modal data. This is achieved by combining simple mechanical testing data, potentially from a distinct material, with digital image correlation-type full-field data acquisition to ultimately enable rapid constitutive modeling discovery. The simplicity of the sparse representation enables easy integration of neural constitutive models in existing finite element workflows, and also enables low-dimensional updating during transfer learning.

本构模型多模态数据有限元稀疏化

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