IMPROVING REDUCED-ORDER ROTATING DETONATION ENGINE MODELS WITH DATA ASSIMILATION AND MACHINE LEARNING

Rotating detonation engines (RDEs) are complex, multiscale combustion devices where detonation waves travel azimuthally around an annulus. While high-fidelity simulations (DNS/LES) capture the necessary physics, they are computationally prohibitive for design and optimization. Reduced-order models, such as the one-dimensional Koch-Kutz model, offer a computationally efficient alternative but lack the expressivity to capture high-frequency wave dynamics and fine-scale thermal structures. This paper addresses this deficit by using continuous data assimilation (nudging) to synchronize the reduced-order model with high-fidelity temperature data. By recording the feedback required to force the reduced model onto the high-fidelity trajectory, the authors generate a state-dependent correction term. They then train a Jacobian-regularized neural network to approximate this correction, enabling the reduced model to operate autonomously with improved accuracy.

The nudging-based data assimilation successfully drives the reduced-order Koch-Kutz solver toward the high-fidelity target, effectively diagnosing the model-form error. The recorded nudging source reveals that the missing physics are concentrated along the detonation-front trajectories. The resulting neural closure, trained using a combination of mean-squared error and a binned spectral-power loss, successfully captures the high-frequency residual. When deployed autonomously, the corrected model recovers the marginal statistics and spatial power spectra of the high-fidelity reference, significantly outperforming the unnudged baseline. The authors also introduce a Jacobian penalty during training to discourage locally amplifying feedback, which helps maintain stability during long-term autonomous rollouts.

This work provides a systematic, non-intrusive framework for improving reduced-order models of complex, multiscale fluid systems. By using data assimilation as a diagnostic tool to extract missing physics, the authors bridge the gap between physically grounded low-order models and data-driven surrogates. This approach is particularly valuable for engineering applications where full-scale high-fidelity simulations are too expensive, but where capturing the statistical behavior of the thermal field is essential for design and performance prediction.