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.

翻译：弥合计算廉价模型与复杂物理系统之间的仿真-现实差距，仍然是机器学习应用于工程问题的核心挑战，在多尺度场景中尤为突出，因为降阶模型通常仅能捕捉主导动力学。在本工作中，我们提出了Cheap2Rich，一个多尺度数据同化框架，通过将快速低保真度先验与可学习的、可解释的差异校正相结合，从稀疏传感器历史数据中重建高保真度状态空间。我们在旋转爆震发动机（RDEs）上验证了该框架的性能，RDEs是一类具有挑战性的系统，其将爆震波前传播与喷注器驱动的非定常性、混合过程以及跨不同尺度的刚性化学反应相耦合。我们的方法成功地从稀疏测量数据中重建了高保真度的RDE状态，同时分离出了与喷注器驱动效应相关的、具有物理意义的差异动力学。研究结果展示了一个适用于复杂多尺度系统中数据同化与系统辨识的通用多保真度框架，该框架能够实现快速设计探索、实时监测与控制，并提供可解释的差异动力学。本项目代码发布于：github.com/kro0l1k/Cheap2Rich。