# Improving Reduced-Order Rotating Detonation Engine Models with Data Assimilation and Machine Learning

arXiv: https://arxiv.org/abs/2609.16237 · HTML: https://mlsanity.com/paper/2609.16237/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 14 Sep 2026.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)](https://mlsanity.com/paper/1911.09145/) (2019)
- [Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons](https://mlsanity.com/paper/2202.06988/) (2022)
- [A posteriori learning for quasi-geostrophic turbulence parametrization](https://mlsanity.com/paper/2204.03911/) (2022)
- [A Perspective on Machine Learning Methods in Turbulence Modelling](https://mlsanity.com/paper/2010.12226/) (2020)
- [Binned Spectral Power Loss for Improved Prediction of Chaotic Systems](https://mlsanity.com/paper/2502.00472/) (2025)
- [Data-driven Modeling of Rotating Detonation Waves](https://mlsanity.com/paper/2008.05586/) (2020)
- [Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Engines](https://mlsanity.com/paper/2601.20295/) (2026)
- [Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics](https://mlsanity.com/paper/2604.23874/) (2026)
- [A TVD neural network closure and application to turbulent combustion](https://mlsanity.com/paper/2408.03413/) (2024)

## Abstract (arXiv)

Rotating detonation engines (RDEs) exhibit strongly nonlinear, multiscale wave dynamics that set the observed thermal field. High-fidelity simulations (DNS/LES) resolve these structures but remain computationally prohibitive, while low-order models such as the one-dimensional Koch-Kutz model capture circumferential wave motion yet lack the expressivity for high-frequency content. We use continuous data assimilation (nudging) to synchronize the Koch-Kutz solver with processed high-fidelity temperature data, introducing the prediction-observation mismatch as a relaxation source in the conserved energy equation; where observations are temporally sparse, interpolation supplies a target at every source update. As the nudging strength increases, the reduced model is progressively drawn onto the high-fidelity trajectory, and the forcing recorded along it provides an explicit, state-dependent estimate of the correction the model requires. We then train a Jacobian-regularized closure a priori on this recorded source. With the observation term removed, the corrected model advances autonomously, remains bounded, and recovers the temperature spectrum and the marginal statistics of the conserved variables relative to the baseline.