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.

翻译：摘要：人工智能赋能的材料本构建模近期进展，已聚焦于从纯数据驱动范式转向物理约束与机理原则的强制执行——这一概念被称为物理增强。经典现象学方法依赖预设模型的选择及其参数标定，而机器学习方法则侧重于模型本身的发现。稀疏回归方法介于两者之间，其在标定过程中对海量预设模型库进行探查。上述范式中的稀疏化，以及神经网络架构层面的稀疏化，已被证明能实现可解释性、不确定性量化，并因所得模型的低维特性而促进异构软件集成。人工智能赋能的材料本构建模领域多数研究仅聚焦单一数据源，但实际中材料建模流程可包含来自多种来源的数据（多模态数据），以及同一材料类别中其他材料测试数据（多保真数据）。本研究提出物理增强有限元模型更新（paFEMU），作为一种迁移学习方法，融合了人工智能赋能的材料本构建模、稀疏化以发现可解释模型、以及利用多模态数据的基于有限元伴随优化技术。其实现方式是将来自不同材料的简单力学测试数据与数字图像相关类全场数据采集相结合，最终实现快速本构模型发现。稀疏表示的简洁性使得神经本构模型能便捷集成至现有有限元工作流中，并支持迁移学习过程中的低维更新。