具有p个参数的动态模型由2p + 1个随机特征识别
Dynamic models with $p$ parameters are identified by $2p+1$ random features
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中文总结 AI 辅助
研究有噪声时间序列动态模型识别，基于无噪声系统识别结果开发类似原理，涵盖多种模型，用洛伦兹 - 63和亨农映射模型说明其效用，可从少量测量恢复系统结构。
中文摘要 AI 辅助
非线性动力学的一个基本原理是，动态系统的结构可以从少量通用测量或坐标中恢复。我们为有噪声的时间序列动态模型识别开发了一个类似原理，它基于无噪声动态系统的先前识别结果。噪声可以是非独立同分布、非高斯且依赖于状态的。我们的结果涵盖有噪声观测的微分方程、离散时间动态系统以及具有过程噪声的随机模型。我们用具有观测噪声的洛伦兹 - 63模型和亨农映射模型说明了这种识别原理的效用。
英文摘要
A foundational principle in nonlinear dynamics is that the structure of a dynamical system can be recovered from a small number of generic measurements or coordinates. We develop an analogous principle for the identification of dynamic models for time series with noise, which builds on previous identification results for noiseless dynamical systems. The noise is allowed to be non-iid, non-Gaussian, and dependent on the state. Our results cover noisily observed differential equations and discrete-time dynamical systems, as well as stochastic models with process noise. We illustrate the utility of this identification principle using a Lorenz-63 model and a Hénon map model, both with observational noise.
发表机构
- Carnegie Mellon University（卡内基梅隆大学）
- Santa Fe Institute（圣塔菲研究所）
机构由 AI 辅助整理，请以论文原文为准。
