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This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics-based modelling. The non-intrusive nature of the approach enables variable transformations that expose system structure. The specific contribution of this paper is to advance the formulation robustness and algorithmic scalability of the Operator Inference approach. Regularisation is introduced to the formulation to avoid over-fitting. The task of determining an optimal regularisation is posed as an optimisation problem that balances training error and stability of long-time integration dynamics. A scalable algorithm and open-source implementation are presented, then demonstrated for a single-injector rocket combustion example. This example exhibits rich dynamics that are difficult to capture with state-of-the-art reduced models. With appropriate regularisation and an informed selection of learning variables, the reduced-order models exhibit high accuracy in repredicting the training regime and acceptable accuracy in predicting future dynamics, while achieving close to a million times speedup in computational cost. When compared to a stateof-the-art model reduction method, the Operator Inference models provide the same or better accuracy at approximately one thousandth of the computational cost.

This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method combines the perspectives of model reduction and machine learning. Model reduction brings in the physics of the problem, constraining the ROM predictions to lie on a subspace defined by the governing equations. This is achieved by defining the ROM in proper orthogonal decomposition (POD) coordinates, which embed the rich physics information contained in solution snapshots of a high-fidelity computational fluid dynamics (CFD) model. The machine learning perspective brings the flexibility to use transformed physical variables to define the POD basis. This is in contrast to traditional model reduction approaches that are constrained to use the physical variables of the high-fidelity code. Combining the two perspectives, the approach identifies a set of transformed physical variables that expose quadratic structure in the combustion governing equations and learns a quadratic ROM from transformed snapshot data. This learning does not require access to the high-fidelity model implementation. Numerical experiments show that the ROM accurately predicts temperature, pressure, velocity, species concentrations, and the limit-cycle amplitude, with speedups of more than five orders of magnitude over high-fidelity models. Moreover, ROM-predicted pressure traces accurately match the phase of the pressure signal and yield good approximations of the limit-cycle amplitude.

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