This paper presents a novel reduced-order model (ROM) based data assimilation framework for parametric high-fidelity time-dependent neutron transport equations (TNTE). The ROM is constructed utilizing affine-parametric operator inference, a scientific machine learning that learns operators of the subspace dynamical system through a non-intrusive data-driven approach. The affine-parametric structure effectively accommodates TNTE with diverse time-varying parameters, obviating the need for interpolation in parameter space and enabling direct mapping of time-varying input parameters to high-fidelity solutions. Compared with the FOM solver in test problems, owing to ROM’s low-rank feature, the ROM yields accurate and rapid solutions with less than 1% relative error and achieves speedups by five or six orders of magnitude. To underscore the efficacy of the operator inference-based ROM within a data assimilation context, the framework is seamlessly integrated with both the linear Kalman filter (KF) and the ensemble Kalman filter (EnKF). Employing a numerical example of a two-dimensional pressurized water nuclear reactor core, the ROM-based KF/EnKF successfully incorporates spatiotemporal information from measurements to correct predictions in the absence of accurate initial conditions or parameters. Furthermore, the method demonstrates a promising capacity for time-varying parameter inference and inverse uncertainty quantification, indicating a significant stride in the field of nuclear reactor core data assimilation.

中文翻译：

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高保真中子输运的算子推理驱动数据同化


本文提出了一种新颖的基于降阶模型（ROM）的参数化高保真瞬态中子输运方程（TNTE）数据同化框架。 ROM 是利用仿射参数算子推理构建的，这是一种科学机器学习，通过非侵入性数据驱动方法学习子空间动力系统的算子。仿射参数结构有效地适应了具有不同时变参数的TNTE，消除了在参数空间中插值的需要，并能够将时变输入参数直接映射到高保真解。与测试问题中的FOM求解器相比，由于ROM的低秩特性，ROM求解准确快速，相对误差小于1%，加速速度提高了五到六个数量级。为了强调数据同化环境中基于算子推理的 ROM 的有效性，该框架与线性卡尔曼滤波器 (KF) 和集成卡尔曼滤波器 (EnKF) 无缝集成。采用二维压水核反应堆堆芯的数值示例，基于 ROM 的 KF/EnKF 成功地将测量中的时空信息结合起来，在缺乏准确的初始条件或参数的情况下正确预测。此外，该方法展示了时变参数推断和逆不确定性量化的良好能力，表明核反应堆堆芯数据同化领域取得了重大进步。