标题： 多尺度热物理的潜在表示学习：应用于冲击多孔 energetic 材料的动力学 显示英文标题

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

摘要： 跨长度和时间尺度的物理耦合在微结构材料对外部载荷的响应中起着重要作用。在一个多尺度框架内，未解析（次网格）的介观尺度动力学通过闭合模型被提升到异质材料的均匀化（宏观尺度）表示中。目前，利用介观尺度模拟数据训练的深度学习模型是一种流行的吸收此类闭合定律的方法。然而，介观尺度模拟计算成本高昂，在从头开始训练基于深度学习的代理模型时提出了实际挑战。在这项工作中，我们研究了一种受自然语言处理中标记化思想启发的替代元学习方法。我们展示了可以通过对涉及典型但复杂的反应动力学问题（例如，\textit{即，也就是说}）中的物理场介观演化过程进行标记化，来学习微观尺度物理的降维表示，从而加速介观尺度的学习过程。\textit{微米}尺度动力学的概率潜在表示被学习为构建块，用于\textit{介观}尺度动力学。\textit{meso-}尺度潜在动力学模型通过对小规模介观尺度模拟数据集的训练，学习相邻构建块之间的相关性。我们将我们的模型性能与仅在完整介观尺度数据集上训练的具有物理感知的递归卷积神经网络（PARC）进行了比较。我们证明了在稀疏介观尺度数据的情况下，我们的模型可以优于PARC。所提出的方法通过利用廉价的微观尺度模拟和小规模介观尺度数据集上的快速训练，加速了闭合模型的发展，并可应用于广泛的多尺度建模问题。 显示英文摘要

摘要： 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.