This paper presents a computationally efficient wavefront aberration prediction framework for data-driven control in large-scale adaptive optics systems. Our novel prediction algorithm splits prediction into two stages: a high-resolution and a low-resolution stage. For the former, we exploit sparsity structures in the system matrices in a data-driven Kalman filtering algorithm and constrain the identified gain to be likewise sparse; for the latter, we identify a dense Kalman gain and perform corrections to the suboptimal predictions of the former on a smaller grid. This novel prediction framework is able to retain the robustness to measurement noise of the standard Kalman filter in a much more computationally efficient manner, in both its offline and online aspects, while minimally sacrificing performance; its data-driven nature further compensates for modeling errors. As an intermediate result, we present a sparsity-exploiting data-driven Kalman filtering algorithm able to quickly estimate an approximate Kalman gain without solving the Riccati equation.

中文翻译：

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用于大规模自适应光学的稀疏数据驱动波前预测

本文提出了一种计算效率高的波前像差预测框架，用于大规模自适应光学系统中的数据驱动控制。我们新颖的预测算法将预测分为两个阶段：高分辨率和低分辨率阶段。对于前者，我们在数据驱动的卡尔曼滤波算法中利用系统矩阵中的稀疏结构，并将识别的增益限制为同样稀疏；对于后者，我们确定了密集的卡尔曼增益，并在较小的网格上对前者的次优预测进行校正。这种新颖的预测框架能够在离线和在线方面以更高效的计算方式保持标准卡尔曼滤波器对测量噪声的鲁棒性，同时最大限度地降低性能；它的数据驱动性质进一步补偿了建模错误。作为中间结果，我们提出了一种利用稀疏性的数据驱动卡尔曼滤波算法，能够在不求解 Riccati 方程的情况下快速估计近似卡尔曼增益。