Learning to Forecast Dynamical Systems from Streaming Data
Learning to Forecast Dynamical Systems from Streaming Data
复制标题
DOI：
10.1137/21m144983x
复制
发表时间：
2021-09
期刊：
影响因子：
--
通讯作者：
D. Giannakis;Amelia Henriksen;J. Tropp;Rachel A. Ward
中科院分区：
文献类型：
--
作者：
D. Giannakis;Amelia Henriksen;J. Tropp;Rachel A. Ward
核模拟预测 (KAF) 是一种强大的方法，用于对动态生成的时间序列数据进行数据驱动的非参数预测。这种方法在库普曼算子理论中有严格的基础，并且在实践中产生了良好的预测，但它受到核方法常见的沉重计算成本的影响。本文提出了一种 KAF 流式算法，只需对训练数据进行一次传递。该算法在不牺牲预测技能的情况下极大地降低了训练和预测的成本。计算实验表明，流式 KAF 方法可以在数据稀缺和数据丰富的情况下成功预测几类动力系统（周期、准周期和混沌）。作为流式内核回归的新模板，整体方法可能会引起更广泛的兴趣。
Kernel analog forecasting (KAF) is a powerful methodology for data-driven, non-parametric forecasting of dynamically generated time series data. This approach has a rigorous foundation in Koopman operator theory and it produces good forecasts in practice, but it suffers from the heavy computational costs common to kernel methods. This paper proposes a streaming algorithm for KAF that only requires a single pass over the training data. This algorithm dramatically reduces the costs of training and prediction without sacrificing forecasting skill. Computational experiments demonstrate that the streaming KAF method can successfully forecast several classes of dynamical systems (periodic, quasi-periodic, and chaotic) in both data-scarce and data-rich regimes. The overall methodology may have wider interest as a new template for streaming kernel regression.