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

TL;DR

Cheap2Rich presents a multi-fidelity data assimilation framework that reconstructs high-fidelity rotating detonation engine states from sparse sensor histories by coupling a fast low-fidelity prior with spectrally constrained high-frequency corrections. The approach decomposes dynamics into a low-frequency backbone aligned to reality via latent-GAN augmentation and a high-frequency residual that is spectrally sparse and physically interpretable, enabling rapid design exploration and real-time monitoring. Quantitatively, the method yields an RMSE reduction of about 80% relative to the baseline on held-out data, while revealing interpretable injector-driven physics through HF corrections and enabling SINDy-based discovery of missing physics terms. The combination of SHRED-based latent learning, adversarial alignment, spectral regularization, and SINDy yields a practical, interpretable surrogate for high-dimensional, multiscale RDE dynamics with broad potential for control and design optimization in complex engineered 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.

Figures (13)

• Figure 1: A rotating detonation rocket engine (RDRE). Full-scale geometry (top left) and cross-sectional schematic with primary dimensions (top right) Temperature and Pressure mid-channel contour projections (bottom).
• Figure 2: The Cheap2Rich architecture. (a) Simulation model provides full-state data $\mathbf{X}$ and sparse sensor measurements $\mathbf{S}$. (b) A standard SHRED network is trained on simulation data to reconstruct full states $\tilde{\mathbf{X}}$ from sensor histories. (c) Deployment on real sensors: the real physics full state $\mathbf{X}'$ is unobserved; only sparse sensor measurements $\mathbf{S}'$ are available. The LF DA-SHRED pathway updates the latent features to reality, producing $\tilde{\mathbf{X}}'_{\text{LF}}$. The HF pathway processes sensor residuals $\mathbf{R}$ to capture fine-scale corrections $\tilde{\mathbf{X}}'_{\text{HF}}$. The final reconstruction $\tilde{\mathbf{X}}'_{\text{LF+HF}}$ combines both pathways to close the simulation-to-reality gap.
• Figure 3: Time evolution of 1d projection of temperature contour before preprocessing (left), and in the COM frame of reference after min-max rescaling (right)
• Figure 4: Temperature field obtained from Koch's model described in Subsection \ref{['subsec:description_of_Koch']} before (left) and after (right) preprocessing.
• Figure 5: Schematic of the Cheap2Rich architecture. The LF pathway learns the dominant dynamics from simulation and aligns to reality via a latent GAN. The HF pathway learns spectrally-sparse corrections from sensor residuals.