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.

翻译：本文聚焦于为非线性混沌等离子体湍流模拟构建非侵入式科学机器学习（SciML）降阶模型（ROMs）。具体而言，我们提出利用算子推理（OpInf）方法从数据中构建低成本的物理降阶模型用于此类模拟。作为代表性案例，我们以用于模拟二维静电流体漂移波等离子体湍流的哈泽川-若谷（HW）方程为研究对象。为全面评估OpInf方法构建该模型精确降阶模型的潜力，我们设置了可产生复杂非线性自驱动动力学的HW方程参数配置，并进行两组实验。首先，我们利用从特定初始条件的HW方程直接数值模拟中获得的数据训练OpInf降阶模型，并预测超出训练时间范围的状态。在更具挑战性的第二组实验中，我们使用相同数据集训练降阶模型，但针对另外六种不同初始条件进行预测。结果表明，OpInf降阶模型能够捕捉湍流动力学的重要特征，并泛化至未见过的初始条件，同时将高保真模型的单核评估时间降低多达五个数量级。在更广泛的聚变研究背景下，这项研究表明非侵入式科学机器学习降阶模型有潜力大幅加速数值研究，最终能够实现优化聚变装置的设计与实时控制等任务。