使用等变自回归储备池计算机识别具有对称性的系统
Identifying Systems with Symmetries using Equivariant Autoregressive Reservoir Computers
AI总结：
本文研究利用等变自回归储备池计算机识别具有对称性的动力系统，通过对称保持时间延迟嵌入与稀疏最小二乘辨识输出耦合矩阵，显著提升了结构化辨识精度。
摘要：
本文所报告的研究聚焦于使用等变自回归储备池计算机识别具有对称性的系统。文中给出了结构化矩阵逼近理论的一般性结果，并探索了一种双重方法。首先，对保持一般对称性的非线性时间延迟嵌入进行了全面考察，这涉及分析从所研究的等变系统中采样的时间序列数据。其次，应用稀疏最小二乘方法来辨识输出耦合矩阵的近似表示。这些矩阵在确定等变系统的非线性自回归表示中起着关键作用。这些矩阵的结构特征由系统固有的对称性集合所决定。本文概述了由所述技术推导出的原型算法，并对其实际应用提供了见解。重点强调了与用于等变动力系统仿真的经典储备池计算方法相比，结构化辨识精度得到了显著提升。
英文摘要：
The investigation reported in this document focuses on identifying systems with symmetries using equivariant autoregressive reservoir computers. General results in structured matrix approximation theory are presented, exploring a two-fold approach. Firstly, a comprehensive examination of generic symmetry-preserving nonlinear time delay embedding is conducted. This involves analyzing time series data sampled from an equivariant system under study. Secondly, sparse least-squares methods are applied to discern approximate representations of the output coupling matrices. These matrices play a critical role in determining the nonlinear autoregressive representation of an equivariant system. The structural characteristics of these matrices are dictated by the set of symmetries inherent in the system. The document outlines prototypical algorithms derived from the described techniques, offering insight into their practical applications. Emphasis is placed on the significant improvement on structured identification precision when compared to classical reservoir computing methods for the simulation of equivariant dynamical systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
