arXiv:2507.19046cs.LG2025-07被引 3

用可视图构建动态感知的储层网络,提升非线性时间序列预测精度。

Dynamics-Informed Reservoir Computing with Visibility Graphs

  • 将时间序列转为可视图,直接生成与任务动态匹配的储层结构
  • 在杜芬振子预测中,相比同规模随机图,预测更准确且结果更稳定
  • 无需调参,适合追求高效可靠的时序预测研究者

复杂非线性时间序列的精确预测在工程与科学领域仍具挑战。储层计算(RC)通过仅训练输出层、固定随机结构的储层网络,提供了一种比传统深度学习更高效的替代方案。然而,其广泛随机的网络结构常导致性能不佳且网络过大,动态机制不明确。为此,本文提出一种动态感知的储层计算(DyRC)框架,通过输入训练序列系统性推导储层网络结构。采用可视图(VG)技术,将时间序列数据转化为网络:以测量点为节点,按相互可见性连接。直接采用训练数据生成的可视图构建储层网络,利用无参数的可视图方法避免昂贵的超参数调优。该过程使储层直接反映所研究预测任务的具体动态特性。我们在经典非线性杜芬振子预测任务上评估了DyRC-VG方法,考察预测精度与一致性。相较于同规模、谱半径和固定密度的埃爾德什-雷尼(ER)图,DyRC-VG表现出更高的预测质量与更一致的重复实现表现。在某些条件下,密度匹配的ER图可超越两者。

原文摘要 · Abstract (English)

Accurate prediction of complex and nonlinear time series remains a challenging problem across engineering and scientific disciplines. Reservoir computing (RC) offers a computationally efficient alternative to traditional deep learning by training only the read-out layer while employing a randomly structured and fixed reservoir network. Despite its advantages, the largely random reservoir graph architecture often results in suboptimal and oversized networks with poorly understood dynamics. Addressing this issue, we propose a novel Dynamics-Informed Reservoir Computing (DyRC) framework that systematically infers the reservoir network structure directly from the input training sequence. This work proposes to employ the visibility graph (VG) technique, which converts time series data into networks by representing measurement points as nodes linked by mutual visibility. The reservoir network is constructed by directly adopting the VG network from a training data sequence, leveraging the parameter-free visibility graph approach to avoid expensive hyperparameter tuning. This process results in a reservoir that is directly informed by the specific dynamics of the prediction task under study. We assess the DyRC-VG method through prediction tasks involving the canonical nonlinear Duffing oscillator, evaluating prediction accuracy and consistency. Compared to an Erdős-Rényi (ER) graph of the same size, spectral radius, and fixed density, we observe higher prediction quality and more consistent performance over repeated implementations in the DyRC-VG. An ER graph with density matched to the DyRC-VG can in some conditions outperform both approaches.

储层计算时间序列可视图动态建模

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