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

arXiv 2506.12996 ↗First posted 15 Jun 2025physics.comp-ph cs.LGcited by 0

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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.

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.

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References · 28

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16 more
  1. 2021Curriculum Learning: A Surveycited by 259
  2. 2020A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEscited by 105
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  16. 2024PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modelingcited by 10

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