# Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Engines

arXiv: https://arxiv.org/abs/2601.20295 · HTML: https://mlsanity.com/paper/2601.20295/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms](https://mlsanity.com/paper/2510.23166/) (2025)
- [Hierarchical Implicit Neural Emulators](https://mlsanity.com/paper/2506.04528/) (2025)
- [Accelerating scientific discovery with the common task framework](https://mlsanity.com/paper/2511.04001/) (2025)
- [Data assimilation and discrepancy modeling with shallow recurrent decoders](https://mlsanity.com/paper/2512.01170/) (2025)
- [A Physics-informed Multi-resolution Neural Operator](https://mlsanity.com/paper/2510.23810/) (2025)
- [Data-driven Modeling of Rotating Detonation Waves](https://mlsanity.com/paper/2008.05586/) (2020)
- [A GPU-based Compressible Combustion Solver for Applications Exhibiting Disparate Space and Time Scales](https://mlsanity.com/paper/2510.23993/) (2025)

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

- [UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression](https://mlsanity.com/paper/2604.01305/) (2026)
- [LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)](https://mlsanity.com/paper/2604.01216/) (2026)
- [Improving Reduced-Order Rotating Detonation Engine Models with Data Assimilation and Machine Learning](https://mlsanity.com/paper/2609.16237/) (2026)

## Abstract (arXiv)

Bridging the sim2real gap between computationally inexpensive models and complex physical systems remains a central challenge in machine learning applications to engineering problems, particularly in multi-scale settings where reduced-order models typically capture only dominant dynamics. In this work, we present Cheap2Rich, a multi-scale data assimilation framework that reconstructs high-fidelity state spaces from sparse sensor histories by combining a fast low-fidelity prior with learned, interpretable discrepancy corrections. We demonstrate the performance on rotating detonation engines (RDEs), a challenging class of systems that couple detonation-front propagation with injector-driven unsteadiness, mixing, and stiff chemistry across disparate scales. Our approach successfully reconstructs high-fidelity RDE states from sparse measurements while isolating physically meaningful discrepancy dynamics associated with injector-driven effects. The results highlight a general multi-fidelity framework for data assimilation and system identification in complex multi-scale systems, enabling rapid design exploration and real-time monitoring and control while providing interpretable discrepancy dynamics. Code for this project is is available at: github.com/kro0l1k/Cheap2Rich.