arXiv:2506.12996physics.comp-phcs.LG2025-06

用微尺度模拟数据加速中尺度学习,提升含能多孔材料冲击响应建模效率。

Latent Representation Learning of Multi-scale Thermophysics: Application to Dynamics in Shocked Porous Energetic Material

  • 将中尺度物理演化视为可分解的'词元',构建概率隐变量表示微尺度动力学。
  • 仅需少量中尺度数据训练,性能超越传统神经网络模型。
  • 适合多尺度建模、计算资源受限场景下的闭包模型快速开发。

跨尺度物理耦合在微结构材料对外载响应中起关键作用。在多尺度框架下,未解析的(亚网格)介观尺度动态通过闭包模型上标到均质化(宏观)材料表征。利用介观尺度仿真数据训练深度学习模型已成为拟合闭包律的流行方法。然而,介观尺度仿真计算成本高,难以从零开始训练基于深度学习的代理模型。本文提出一种受自然语言处理中分词思想启发的元学习方法:针对典型但复杂的反应动力学问题——多孔含能材料中的冲击诱导能量局域化,将介观尺度物理场演化进行分词处理,学习其微尺度物理的概率隐表示作为介观尺度动力学的构建模块。介观尺度隐变量动力学模型通过在小规模介观尺度仿真数据上训练,学习相邻模块间的关联。与仅使用完整介观尺度数据训练的物理感知循环卷积神经网络(PARC)相比,本模型在数据稀缺条件下表现更优。该方法通过低成本微尺度仿真和小样本介观尺度训练,显著加速闭包模型开发,适用于多种多尺度建模问题。

原文摘要 · Abstract (English)

Coupling of physics across length and time scales plays an important role in the response of microstructured materials to external loads. In a multi-scale framework, unresolved (subgrid) meso-scale dynamics is upscaled to the homogenized (macro-scale) representation of the heterogeneous material through closure models. Deep learning models trained using meso-scale simulation data are now a popular route to assimilate such closure laws. However, meso-scale simulations are computationally taxing, posing practical challenges in training deep learning-based surrogate models from scratch. In this work, we investigate an alternative meta-learning approach motivated by the idea of tokenization in natural language processing. We show that one can learn a reduced representation of the micro-scale physics to accelerate the meso-scale learning process by tokenizing the meso-scale evolution of the physical fields involved in an archetypal, albeit complex, reactive dynamics problem, \textit{viz.}, shock-induced energy localization in a porous energetic material. A probabilistic latent representation of \textit{micro}-scale dynamics is learned as building blocks for \textit{meso}-scale dynamics. The \textit{meso-}scale latent dynamics model learns the correlation between neighboring building blocks by training over a small dataset of meso-scale simulations. We compare the performance of our model with a physics-aware recurrent convolutional neural network (PARC) trained only on the full meso-scale dataset. We demonstrate that our model can outperform PARC with scarce meso-scale data. The proposed approach accelerates the development of closure models by leveraging inexpensive micro-scale simulations and fast training over a small meso-scale dataset, and can be applied to a range of multi-scale modeling problems.

多尺度建模隐变量表示元学习含能材料

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