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

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.

High-fidelity simulation for rotating detonation engines requires months of supercomputer time for a single design, because the physics spans scales from tiny fuel injectors to large-scale detonation waves traveling at supersonic speeds. Faster simplified models exist but miss important small-scale effects, creating a fidelity gap. We present Cheap2Rich, a machine learning framework that starts from a fast, rough simulation and uses just sparse sensor measurements to reconstruct what the expensive simulation would have produced. The key idea is to separate the reconstruction into large-scale features the cheap model already captures and small-scale corrections it misses, then learn each part independently. The framework also automatically discovers interpretable equations that describe the missing physics. This could enable engineers to rapidly explore engine designs and monitor operating engines in real time - tasks that are currently bottlenecked by simulation cost. While demonstrated on rocket engines, the approach applies to any setting where cheap models must be reconciled with complex reality using limited measurements.