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

TL;DR

This paper introduces a meta-learning approach using tokenization to learn reduced micro-scale physics representations, significantly accelerating the training of surrogate models for multi-scale thermophysical simulations.

Contribution

It proposes a novel tokenization-based meta-learning method to efficiently learn micro-scale dynamics, reducing data requirements and training time for multi-scale modeling.

Findings

The model outperforms physics-aware recurrent CNN with limited data.

It accelerates micro-scale simulation-based closure model development.

The approach is applicable to various multi-scale problems.

Abstract

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.