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

arXiv: https://arxiv.org/abs/2506.12996 · HTML: https://mlsanity.com/paper/2506.12996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 97 references that are in the map.
- First posted on arXiv 15 Jun 2025.

## Builds on (most cited first, 28 of 28)

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- [Rethinking materials simulations: Blending direct numerical simulations with neural operators](https://mlsanity.com/paper/2312.05410/) (2023)
- [Improving physics-informed neural networks with meta-learned optimization](https://mlsanity.com/paper/2303.07127/) (2023)
- [PARC: Physics-Aware Recurrent Convolutional Neural Networks to Assimilate Meso-scale Reactive Mechanics of Energetic Materials](https://mlsanity.com/paper/2204.07234/) (2022)
- [PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling](https://mlsanity.com/paper/2402.12503/) (2024)

## Abstract (arXiv)

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, textitviz., shock-induced energy localization in a porous energetic material. A probabilistic latent representation of textitmicro-scale dynamics is learned as building blocks for textitmeso-scale dynamics. The textitmeso-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.