# PARC: Physics-Aware Recurrent Convolutional Neural Networks to Assimilate Meso-scale Reactive Mechanics of Energetic Materials

arXiv: https://arxiv.org/abs/2204.07234 · HTML: https://mlsanity.com/paper/2204.07234/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 78 references that are in the map.
- First posted on arXiv 4 Apr 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems](https://mlsanity.com/paper/1901.04878/) (2019)
- [Deep learning for synthetic microstructure generation in a materials-by-design framework for heterogeneous energetic materials](https://mlsanity.com/paper/2004.04814/) (2020)
- [Deep segmentation networks predict survival of non-small cell lung cancer](https://mlsanity.com/paper/1903.11593/) (2019)

## Built on by (most cited first, 11 of 11)

- [PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling](https://mlsanity.com/paper/2402.12503/) (2024)
- [Towards a Physics Foundation Model](https://mlsanity.com/paper/2509.13805/) (2025)
- [Challenges and opportunities for machine learning in multiscale computational modeling](https://mlsanity.com/paper/2303.12261/) (2023)
- [3D Neural Operator-Based Flow Surrogates around 3D geometries: Signed Distance Functions and Derivative Constraints](https://mlsanity.com/paper/2503.17289/) (2025)
- [Multi-Task Multi-Fidelity Learning of Properties for Energetic Materials](https://mlsanity.com/paper/2408.14488/) (2024)
- [Data Fusion of Deep Learned Molecular Embeddings for Property Prediction](https://mlsanity.com/paper/2504.07297/) (2025)
- [Reduced Order Modeling of Energetic Materials Using Physics-Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)](https://mlsanity.com/paper/2509.12401/) (2025)
- [A physics-aware deep learning model for shear band formation around collapsing pores in shocked reactive materials](https://mlsanity.com/paper/2510.09670/) (2025)
- [Latent Representation Learning of Multi-scale Thermophysics: Application to Dynamics in Shocked Porous Energetic Material](https://mlsanity.com/paper/2506.12996/) (2025)
- [Generative Chemical Language Models for Energetic Materials Discovery](https://mlsanity.com/paper/2604.03304/) (2026)
- [SimCast-S2S: A Computationally Efficient Diffusion Model for Subseasonal Precipitation Forecasting](https://mlsanity.com/paper/2608.26594/) (2026)

## Abstract (arXiv)

The thermo-mechanical response of shock-initiated energetic materials (EM) is highly influenced by their microstructures, presenting an opportunity to engineer EM microstructure in a "materials-by-design" framework. However, the current design practice is limited, as a large ensemble of simulations is required to construct the complex EM structure-property-performance linkages. We present the Physics-Aware Recurrent Convolutional (PARC) Neural Network, a deep-learning algorithm capable of learning the mesoscale thermo-mechanics of EM from a modest number of high-resolution direct numerical simulations (DNS). Validation results demonstrated that PARC could predict the themo-mechanical response of shocked EM with a comparable accuracy to DNS but with notably less computation time. The physics awareness of PARC enhances its modeling capabilities and generalizability, especially when challenged in unseen prediction scenarios. We also demonstrate that visualizing the artificial neurons at PARC can shed light on important aspects of EM thermos-mechanics and provide an additional lens for conceptualizing EM.