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

2025-06-15

AI Summary

Modeling micro–mesoscale dynamic coupling in porous energetic materials under impact loading is computationally expensive, and mesoscale simulation data are scarce. Method: This paper proposes a meta-learning framework based on probabilistic latent representations. Drawing inspiration from tokenization in natural language processing, it introduces reusable dynamical latent tokens derived from microscale simulations; these tokens are then integrated via few-shot mesoscale data to learn inter-token dependencies for efficient closure modeling. The approach synergistically combines probabilistic latent-variable modeling, meta-learning, and a lightweight latent dynamical network. Contribution/Results: With only minimal mesoscale data, the method significantly outperforms the physics-aware recurrent convolutional network (PARC) trained on full datasets, drastically accelerating closure model development. Moreover, it exhibits strong generalizability across diverse multiscale thermal–mechanical scenarios, enabling robust, data-efficient, and transferable multiscale modeling.

Technology Category

• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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, extit{viz.}, shock-induced energy localization in a porous energetic material. A probabilistic latent representation of extit{micro}-scale dynamics is learned as building blocks for extit{meso}-scale dynamics. The extit{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.

Problem

• Learning multi-scale thermophysics latent representations
• Accelerating meso-scale learning via micro-scale tokenization
• Developing closure models with limited meso-scale data

Innovation

• Tokenization of meso-scale physical field evolution
• Probabilistic latent representation of micro-scale dynamics
• Fast training with small meso-scale dataset