Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference -- a methodology within scientific machine learning that enables learning from data a low-dimensional representation of a high-dimensional system governed by nonlinear partial differential equations -- by embedding such state constraints in the reduced-order model predictions. In the model learning process, we propose a new way to choose regularization hyperparameters based on a key performance indicator. Since embedding state constraints improves the stability of the Operator Inference reduced-order model, we compare the proposed state constraints-embedded Operator Inference with the standard Operator Inference and other stability-enhancing approaches. For an application to char combustion, we demonstrate that the proposed approach yields state predictions superior to the other methods regarding stability and accuracy. It extrapolates over 200\% past the training regime while being computationally efficient and physically consistent.

This paper focuses on the construction of non-intrusive Scientific Machine Learning (SciML) Reduced-Order Models (ROMs) for nonlinear, chaotic plasma turbulence simulations. In particular, we propose using Operator Inference (OpInf) to build low-cost physics-based ROMs from data for such simulations. As a representative example, we focus on the Hasegawa-Wakatani (HW) equations used for modeling two-dimensional electrostatic drift-wave plasma turbulence. For a comprehensive perspective of the potential of OpInf to construct accurate ROMs for this model, we consider a setup for the HW equations that leads to the formation of complex, nonlinear, and self-driven dynamics, and perform two sets of experiments. We first use the data obtained via a direct numerical simulation of the HW equations starting from a specific initial condition and train OpInf ROMs for predictions beyond the training time horizon. In the second, more challenging set of experiments, we train ROMs using the same dataset as before but this time perform predictions for six other initial conditions. Our results show that the OpInf ROMs capture the important features of the turbulent dynamics and generalize to new and unseen initial conditions while reducing the evaluation time of the high-fidelity model by up to five orders of magnitude in single-core performance. In the broader context of fusion research, this shows that non-intrusive SciML ROMs have the potential to drastically accelerate numerical studies, which can ultimately enable tasks such as the design and real-time control of optimized fusion devices.