提出新算法，可精准学习具有有限稳定模式的非线性动态系统。
Universal Learning of Nonlinear Dynamics
- 基于谱滤波技术，从历史观测预测未来状态。
- 对任意有限稳定模式系统实现预测误差趋零，速率由新可学习性度量决定。
- 首次统一处理非对称、带噪声的稳定系统，适合控制与机器学习研究者。
我们研究了学习一个边缘稳定未知非线性动力系统的根本问题。提出一种基于谱滤波的技术算法，通过系统谱表示，将过去观测映射到下一时刻状态。利用在线凸优化技术，证明了对任何具有有限个边缘稳定模态的非线性动力系统，预测误差可趋于零，其收敛速率由一个新颖的量化控制论可学习性概念决定。该方法的核心是针对线性动力系统的新型谱滤波算法，能融合历史观测并适用于一般带噪声和边缘稳定的系统。这显著扩展了原始谱滤波算法，支持非对称动态及噪声校正，具备独立研究价值。
原文摘要 · Abstract (English)
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonlinear dynamical system that has finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This significantly generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.
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