# Revealing Low-Dimensional Structure in 2D Richtmyer-Meshkov Instabilities via Parametric Reduced-Order Modeling

arXiv: https://arxiv.org/abs/2510.16197 · HTML: https://mlsanity.com/paper/2510.16197/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 58 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems](https://mlsanity.com/paper/2010.14685/) (2020)
- [JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows](https://mlsanity.com/paper/2203.13760/) (2022)
- [GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder](https://mlsanity.com/paper/2308.05882/) (2023)
- [A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling](https://mlsanity.com/paper/2403.10748/) (2024)
- [On latent dynamics learning in nonlinear reduced order modeling](https://mlsanity.com/paper/2408.15183/) (2024)
- [High-Precision Inversion of Dynamic Radiography Using Hydrodynamic Features](https://mlsanity.com/paper/2112.01627/) (2021)
- [Physics-Driven Learning of Wasserstein GAN for Density Reconstruction in Dynamic Tomography](https://mlsanity.com/paper/2110.15424/) (2021)
- [Reconstructing Richtmyer-Meshkov instabilities from noisy radiographs using low dimensional features and attention-based neural networks](https://mlsanity.com/paper/2408.00985/) (2024)
- [Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions](https://mlsanity.com/paper/2412.20192/) (2024)
- [Learning Robust Features for Scatter Removal and Reconstruction in Dynamic ICF X-Ray Tomography](https://mlsanity.com/paper/2408.12766/) (2024)
- [Causal Multi-fidelity Surrogate Forward and Inverse Models for ICF Implosions](https://mlsanity.com/paper/2509.05510/) (2025)

## Abstract (arXiv)

Efficient modeling of the Richtmyer-Meshkov instability (RMI) is essential to many engineering tasks, including high-speed combustion and drive and capsule geometry optimization in Inertial Confinement Fusion (ICF). In the latter, RMI causes the ablator and fuel to mix, introducing cold spots into the fuel and lowering performance; controlling RMI is thus a core ICF design concern. In this work, we introduce a reduced-order model for two-dimensional RMI based on the Latent Space Dynamics Identification (LaSDI) algorithm. We demonstrate the efficacy of the proposed methodology in efficiently parametrizing the solution space over a high-dimensional parameter vector consisting of material EOS parameters and initial conditions known to affect RMI growth rates. Using only late-time partial observations of the dynamics, we use our framework to not only provide a highly efficient dynamic surrogate model, but to reveal that the RMI exhibits the structure of a surprisingly low-dimensional and linear dynamical system, into the nonlinear growth regime, after a suitable nonlinear transformation is applied to the material interface, which we approximate as a trained autoencoder. Our use of practical observables and fundamental parameters suggests that such ROMs may be useful for downstream engineering tasks which confront the RMI, while the low-dimensional representation suggests a new direction for theoretical work.