# Using Conservation Laws to Infer Deep Learning Model Accuracy of Richtmyer-meshkov Instabilities

arXiv: https://arxiv.org/abs/2208.11477 · HTML: https://mlsanity.com/paper/2208.11477/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Kornia: an Open Source Differentiable Computer Vision Library for PyTorch](https://mlsanity.com/paper/1910.02190/) (2019)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [Enabling Machine Learning-Ready HPC Ensembles with Merlin](https://mlsanity.com/paper/1912.02892/) (2019)

## Built on by (most cited first, 3 of 3)

- [Learning Physical Models that Can Respect Conservation Laws](https://mlsanity.com/paper/2302.11002/) (2023)
- [Machine Learning Visualization Tool for Exploring Parameterized Hydrodynamics](https://mlsanity.com/paper/2406.15509/) (2024)
- [Spatio-temporal, multi-field deep learning of shock propagation in meso-structured media](https://mlsanity.com/paper/2509.16139/) (2025)

## Abstract (arXiv)

Richtmyer-Meshkov Instability (RMI) is a complicated phenomenon that occurs when a shockwave passes through a perturbed interface. Over a thousand hydrodynamic simulations were performed to study the formation of RMI for a parameterized high velocity impact. Deep learning was used to learn the temporal mapping of initial geometric perturbations to the full-field hydrodynamic solutions of density and velocity. The continuity equation was used to include physical information into the loss function, however only resulted in very minor improvements at the cost of additional training complexity. Predictions from the deep learning model appear to accurately capture temporal RMI formations for a variety of geometric conditions within the domain. First principle physical laws were investigated to infer the accuracy of the model's predictive capability. While the continuity equation appeared to show no correlation with the accuracy of the model, conservation of mass and momentum were weakly correlated with accuracy. Since conservation laws can be quickly calculated from the deep learning model, they may be useful in applications where a relative accuracy measure is needed.