  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 modeling. 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. Regularization is introduced to the formulation to avoid
over-fitting. The task of determining an optimal regularization is posed as an
optimization 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 regularization and an
informed selection of learning variables, the reduced-order models exhibit high
accuracy in re-predicting 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 state-of-the-art model reduction method,
the Operator Inference models provide the same or better accuracy at
approximately one thousandth of the computational cost.
