# A physics-aware deep learning model for energy localization in multiscale shock-to-detonation simulations of heterogeneous energetic materials

arXiv: https://arxiv.org/abs/2211.04561 · HTML: https://mlsanity.com/paper/2211.04561/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [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 learning for synthetic microstructure generation in a materials-by-design framework for heterogeneous energetic materials](https://mlsanity.com/paper/2004.04814/) (2020)
- [Structure and Performance of Fully Connected Neural Networks: Emerging Complex Network Properties](https://mlsanity.com/paper/2107.14062/) (2021)

## Built on by (most cited first, 7 of 7)

- [PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling](https://mlsanity.com/paper/2402.12503/) (2024)
- [Challenges and opportunities for machine learning in multiscale computational modeling](https://mlsanity.com/paper/2303.12261/) (2023)
- [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)
- [Spatio-temporal, multi-field deep learning of shock propagation in meso-structured media](https://mlsanity.com/paper/2509.16139/) (2025)

## Abstract (arXiv)

Predictive simulations of the shock-to-detonation transition (SDT) in heterogeneous energetic materials (EM) are vital to the design and control of their energy release and sensitivity. Due to the complexity of the thermo-mechanics of EM during the SDT, both macro-scale response and sub-grid mesoscale energy localization must be captured accurately. This work proposes an efficient and accurate multiscale framework for SDT simulations of EM. We introduce a new approach for SDT simulation by using deep learning to model the mesoscale energy localization of shock-initiated EM microstructures. The proposed multiscale modeling framework is divided into two stages. First, a physics-aware recurrent convolutional neural network (PARC) is used to model the mesoscale energy localization of shock-initiated heterogeneous EM microstructures. PARC is trained using direct numerical simulations (DNS) of hotspot ignition and growth within microstructures of pressed HMX material subjected to different input shock strengths. After training, PARC is employed to supply hotspot ignition and growth rates for macroscale SDT simulations. We show that PARC can play the role of a surrogate model in a multiscale simulation framework, while drastically reducing the computation cost and providing improved representations of the sub-grid physics. The proposed multiscale modeling approach will provide a new tool for material scientists in designing high-performance and safer energetic materials.