This paper investigates non-intrusive Scientific Machine Learning (SciML) Reduced-Order Models (ROMs) for plasma turbulence simulations. In particular, we focus on Operator Inference (OpInf) to build low-cost physics-based ROMs from data for such simulations. As a representative example, we consider the (classical) Hasegawa-Wakatani (HW) equations used for modeling two-dimensional electrostatic drift-wave turbulence. For a comprehensive perspective of the potential of OpInf to construct predictive ROMs, we consider three setups for the HW equations by varying a key parameter, namely the adiabaticity coefficient. These setups lead to the formation of complex and nonlinear dynamics, which makes the construction of predictive 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, that is, $400\%$ more than the training horizon. Our results show that the OpInf ROMs capture important statistical 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：本文研究了用于等离子体湍流模拟的非侵入式科学机器学习（SciML）降阶模型（ROMs）。具体而言，我们重点关注算子推断（OpInf）方法，旨在利用数据为此类模拟构建低成本的基于物理的降阶模型。作为一个代表性示例，我们考虑了用于模拟二维静电漂移波湍流的（经典）Hasegawa-Wakatani（HW）方程组。为了全面评估OpInf构建预测性降阶模型的潜力，我们通过改变一个关键参数（即绝热系数）来考虑HW方程组的三种设置。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预测性降阶模型都具有挑战性。我们通过对HW方程组进行直接数值模拟来生成训练数据集，并在湍流阶段记录$100$个时间单位内计算得到的状态数据和输出。然后，我们使用这些数据集构建OpInf降阶模型，用于预测后续$400$个时间单位，即比训练时间范围长$400\%$。我们的结果表明，OpInf降阶模型捕捉了湍流动力学的重要统计特征，并能推广到训练时间范围之外，同时将高保真模拟的计算量减少了多达五个数量级。在聚变研究的更广泛背景下，这表明非侵入式SciML降阶模型具有大幅加速数值研究的潜力，最终可能实现诸如优化聚变装置设计等任务。