arXiv:2606.22765cs.NEcs.AI2026-06

通过进化优化揭示预测任务下动态网络的结构约束。

Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos

论文配图:Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos
图 1 · 摘自论文原文
  • 用进化算法优化五种网络参数,提升预测能力
  • 预测误差降低,预报时长延长,效率与精度共存
  • 适合研究自适应动力系统与生物计算机制

生物系统在波动环境中通过将过去刺激转化为内部动态状态来支持未来响应。水库计算提供了类比,但传统方法通常将循环结构视为固定随机网络,仅训练读出层。本文以时空混沌的Kuramoto-Sivashinsky方程为测试平台,对五个构造超参数(规模、连通度、谱半径、输入缩放、读出正则化)进行进化选择,以优化预测性能。进化显著降低了群体预测误差,延长了低误差预报时间窗口,并在设计空间中形成递减收益的规模-效率边界。结构分析显示,进化的水库保持在类似随机块模型的谱包络内,精细调整低特征值模式,将模块性锁定在中间频带,并在此频带内削减连接代价。帕累托分析表明,优秀水库在成本-模块性平面上占据水平底端,说明准确性和效率是协同实现而非简单权衡。结果表明,进化优化不仅提升预测性能,更揭示了循环结构的可解释性约束:稳定适合任务的动力学类别,并优化最相关的架构自由度。因此,进化水库计算为研究预测需求如何塑造自适应动力网络提供了一种受生物启发的框架。

原文摘要 · Abstract (English)

Biological systems maintain function in fluctuating environments by transforming past stimulation into internal dynamical states that support future-oriented responses. Reservoir computing provides a computational analogue, but standard formulations often treat the recurrent substrate as a fixed random network and train only the readout. Here we ask how the substrate itself changes when reservoir architecture is placed under evolutionary selection for prediction. Using the Kuramoto--Sivashinsky equation as a testbed for spatiotemporal chaos, we evolved reservoirs over five construction hyperparameters: size, connectivity degree, spectral radius, input scaling, and readout regularization. Evolution reduced prediction error at the population level, extended the low-error forecast horizon, and organized the design space along a diminishing-return size--efficiency frontier. Structural analyses showed that evolved reservoirs remained within a conserved stochastic-block-model-like spectral envelope while refining low-eigenvalue modes, locking modularity to an intermediate band, and pruning connection cost within that band. Pareto analysis showed that elite reservoirs occupied a horizontal floor in the cost--modularity plane, indicating that accuracy and efficiency were achieved jointly rather than through a simple trade-off. These findings show that evolutionary optimization does not merely improve prediction, but exposes interpretable structural constraints on the recurrent substrate: it stabilizes a task-suitable dynamical class and refines the architectural degrees of freedom most relevant for prediction. Evolutionary reservoir computing therefore provides a bio-inspired framework for studying how predictive demands shape adaptive dynamical networks.

动态网络进化计算预测建模

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