用确定性结构的最小化网络，比随机初始化的网络更好学混沌系统。
Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics
- 用简单规则生成确定性初始结构的最小化回声状态网络（MESN）
- 在90多个混沌系统上误差降低41%，且结果更稳定
- 适合需要高稳定性与可复用性的混沌系统建模任务
机器学习广泛用于建模混沌系统。回声状态网络（ESNs）因其构造简单、训练快速而备受关注。然而，其性能对超参数和随机初始化极为敏感。本文展示，基于确定性规则与简单拓扑构建的最小化确定性回声状态网络（MESN）在重构混沌吸引子任务中优于标准ESN。我们使用超过90个混沌系统的数据集，评估了10种不同的最小化确定性储备池初始化方法。结果表明，MESN相比标准ESN误差最高可降低41%。此外，MESN表现出更少的运行间差异，且超参数可在不同系统间复用。研究说明，在学习混沌动态时，结构化的简单性可超越随机复杂性。
原文摘要 · Abstract (English)
Machine learning (ML) is widely used to model chaotic systems. Among ML approaches, echo state networks (ESNs) have received considerable attention due to their simple construction and fast training. However, ESN performance is highly sensitive to hyperparameter choices and to its random initialization. In this work, we demonstrate that ESNs constructed using deterministic rules and simple topologies (MESNs) outperform standard ESNs in the task of chaotic attractor reconstruction. We use a dataset of more than 90 chaotic systems to benchmark 10 different minimal deterministic reservoir initializations. We find that MESNs obtain up to a 41% reduction in error compared to standard ESNs. Furthermore, we show that the MESNs are more robust, exhibiting less inter-run variation, and have the ability to reuse hyperparameters across different systems. Our results illustrate how structured simplicity in ESN design can outperform stochastic complexity in learning chaotic dynamics.
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