This paper focuses on the construction of non-intrusive Scientific Machine Learning (SciML) Reduced-Order Models (ROMs) for 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 turbulence. For a comprehensive perspective of the potential of OpInf to construct accurate ROMs, we consider three setups for the HW equations by varying a key model parameter, namely the adiabaticity coefficient. These setups lead to the formation of complex and nonlinear dynamics, which makes the construction of accurate ROMs of any kind challenging. We generate the training datasets by performing direct numerical simulations of the HW equations and recording the computed state data and outputs the over a time horizon of 100 time units in the turbulent phase. We then use these datasets to construct OpInf ROMs for predictions over 400 additional time units. Our results show that the OpInf ROMs capture the important features of the turbulent dynamics and generalize beyond the training time horizon while reducing the computational effort of the high-fidelity simulation by up to five orders of magnitude. 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 of optimized fusion devices.

翻译：本文聚焦于为等离子体湍流模拟构建非侵入式的科学机器学习降阶模型。具体而言，我们提出使用算子推断方法，基于此类模拟的数据建立低成本的、基于物理的降阶模型。作为一个代表性示例，我们重点研究了用于模拟二维静电漂移波湍流的Hasegawa-Wakatani方程。为了全面评估算子推断方法构建精确降阶模型的潜力，我们通过改变一个关键模型参数（即绝热系数）来考虑HW方程的三种设置。这些设置导致了复杂且非线性的动力学形成，这使得构建任何类型的精确降阶模型都具有挑战性。我们通过对HW方程进行直接数值模拟来生成训练数据集，并在湍流阶段的100个时间单位内记录计算得到的状态数据和输出。随后，我们利用这些数据集构建算子推断降阶模型，用于对未来400个时间单位进行预测。我们的结果表明，算子推断降阶模型能够捕捉湍流动力学的重要特征，并在训练时间范围之外具有良好的泛化能力，同时将高保真模拟的计算量降低了多达五个数量级。在更广泛的聚变研究背景下，这表明非侵入式的科学机器学习降阶模型具有大幅加速数值研究的潜力，最终能够支持诸如优化聚变装置设计等任务。