论文标题
桥接数据科学和动态系统理论
Bridging data science and dynamical systems theory
论文作者
论文摘要
这篇简短的评论描述了动态系统中统计分析和预测的数学技术。讨论了两个问题，即（i）预测在预测初始化时可能不完整的观察结果下观察到的监督学习问题； （ii）无监督的学习问题，即具有连贯的动力学进化的系统可观察到的系统。我们讨论了从运营商理论上的千古理论与统计学习理论相结合的思想如何为解决这些问题提供了有效的途径，从而导致方法很好地适应了处理非线性动力学，并且随着培训数据的增加，融合可以保证。
This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning problem of forecasting the time evolution of an observable under potentially incomplete observations at forecast initialization; and (ii) the unsupervised learning problem of identification of observables of the system with a coherent dynamical evolution. We discuss how ideas from from operator-theoretic ergodic theory combined with statistical learning theory provide an effective route to address these problems, leading to methods well-adapted to handle nonlinear dynamics, with convergence guarantees as the amount of training data increases.
