تقرير
Identifying Systems with Symmetries using Equivariant Autoregressive Reservoir Computers
| العنوان: | Identifying Systems with Symmetries using Equivariant Autoregressive Reservoir Computers |
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| المؤلفون: | Vides, Fredy, Nogueira, Idelfonso B. R., Banegas, Lendy, Flores, Evelyn |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Electrical Engineering and Systems Science - Systems and Control, Computer Science - Machine Learning, Mathematics - Optimization and Control |
| الوصف: | 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 pivotal 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 their effectiveness in the identification and predictive simulation of equivariant nonlinear systems, regardless of whether such systems exhibit chaotic behavior. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.09511 |
| رقم الأكسشن: | edsarx.2311.09511 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |