We devise a fast algorithm for the gradient of the long-time-average statistics of chaotic systems, with cost almost independent of the number of parameters. It runs on one sample orbit; its cost is linear to the unstable dimension. The algorithm is based on two theoretical results in this paper: the adjoint shadowing lemma for the shadowing contribution and the fast adjoint formula for the unstable divergence in the linear response.

翻译：我们为混乱系统长期平均统计数据的梯度设计了一个快速算法,其成本几乎与参数数量无关。它运行在一个样本轨道上;其成本是线性到不稳定的维度。算法基于本文的两个理论结果:影子贡献的双影性低位和线性反应不稳定差异的快速联合公式。