超越混沌边缘：水库预测中的稳定性-表现力转移
Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting
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中文总结 AI 辅助
研究探索水库预测中混沌边缘启发式方法与机器性能的关系，以谱半径为控制参数，通过分析教师驱动水库集体动力学，提出稳定性-表现力转移指数，能准确识别不同情况下自主预测的最佳谱半径。
中文摘要 AI 辅助
长期以来，混沌边缘启发式方法一直是设计水库计算机的指导原则，但其与机器性能的相关性仍不明确。本文以水库网络的谱半径作为控制参数，表明产生最佳预测性能的半径与孤立、教师驱动或闭环生成水库的李雅普诺夫边缘不一致。通过分析教师驱动水库的集体动力学，发现目标动力学主要由稳定的李雅普诺夫模式表示，其有限时间稳定性受输入强烈调制。这一发现催生了一个稳定性-表现力转移指数，该指数平衡了这些模式在表示目标时的稳定性和表现力。在混沌和准周期目标以及非对称和对称水库中，该指数都能准确识别自主预测的最佳谱半径。
英文摘要
The edge-of-chaos heuristic has long served as a guiding principle for designing reservoir computers, yet its relevance to machine performance remains elusive. Here, taking the spectral radius of the reservoir network as the control parameter, we show that the radius yielding the best forecasting performance does not coincide with the Lyapunov edge of the isolated, teacher-forced, or closed-loop generative reservoir. By analyzing the collective dynamics of the teacher-forced reservoir, we find that the target dynamics are represented mainly by stable Lyapunov modes whose finite-time stability is strongly modulated by the input. This finding motivates a stability-expressivity transfer index, which balances the stability of these modes against their expressivity in representing the target. Across chaotic and quasiperiodic targets, and for both asymmetric and symmetric reservoirs, this index accurately identifies the optimal spectral radius for autonomous forecasting.
发表机构
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China（物理与信息技术学院，陕西师范大学，西安710062，中国）
机构由 AI 辅助整理，请以论文原文为准。
