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

TL;DR

Cheap2Rich introduces a multi-fidelity data assimilation framework that reconstructs high-fidelity states of complex multi-scale systems like rotating detonation engines from sparse data, enabling real-time monitoring, control, and interpretability.

Contribution

The paper presents a novel multi-fidelity framework combining low-fidelity models with learned discrepancy corrections for data assimilation in complex systems.

Findings

Successfully reconstructs high-fidelity RDE states from sparse measurements

Isolates physically meaningful discrepancy dynamics related to injector effects

Enables rapid design, real-time monitoring, and control of multi-scale systems

Abstract

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.