混合化多尺度和延迟储库计算,用于长期准确的混乱系统预测.
1Guangxi Normal University, Guangxi Normal University, Guangxi Key Laboratory of Brain-Inspired Computing and Intelligent Chips, College of Electronic and Information Engineering, Guilin 541004, China and Key Laboratory of Nonlinear Circuits and Optical Communications (, ), Education Department of Guangxi Zhuang Autonomous Region, Guilin, China.
Physical review. E
|January 21, 2026
概括
一种新的混合多尺度延迟储计算 (HyMS-DRC) 方法通过整合多尺度特征和延迟反来改善混乱系统预测,优于准确的长期预测的现有技术.
科学领域:
- 非线性动力学和复杂系统科学.
- 计算神经科学和机器学习.
- 时间序列分析和预测.
背景情况:
- 混沌动态系统对初始条件和多尺度时间动态表现出极度的敏感性,这给预测带来了重大挑战.
- 传统的储水库计算 (RC) 和延迟反储水库计算 (DRC) 是有前途的,但往往无法捕获复杂的多层次特征.
- 现有的多尺度方法 (MS-RC,MS-DRC) 改善了特征表示,但在长期预测方面仍然存在局限性.
研究的目的:
- 引入一种新的混合多尺度延迟水库计算 (HyMS-DRC) 框架,旨在增强混乱系统预测.
- 解决现有的RC方法在捕捉多尺度动态和减轻内存色方面的局限性.
- 为了评估HyMS-DRC的性能与规范混乱系统的既定方法相比.
主要方法:
- 开发了一个并行多尺度架构,集成标准RC和延迟反RC.
- 实现了状态融合,以增强跨时间尺度的动态表示,并对抗记忆色.
- 在双滚,洛伦茨和罗斯勒混乱系统上系统地评估了HyMS-DRC,与RC,DRC,MS-RC和MS-DRC进行比较.
主要成果:
- HyMS-DRC实现了卓越的预测性能,产生了最低的0.0089,0.0137和0.0662.2的正常化根平均平方误差 (NRMSEs).
- 该框架展示了最长的有效预测时间:测试系统的约27.85,24.29和22.37.
- 长期的统计分析证实了强大的吸引子几何结构重建和精确的功率光谱分布复制.
结论:
- 拟议的HyMS-DRC框架显著增强了时间记忆和特征表示在储库中的功能.
- 将多尺度结构与延迟反结合起来,对于准确和强大的混乱系统的长期预测至关重要.
- 对于复杂的非线性动态,HyMS-DRC表现出极好的概括和建模能力.
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