无需先验结构，利用池化计算实现对未见状态空间的泛化建模。
Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing
- 基于多轨迹训练策略，提升池化计算模型对分散数据的利用效率。
- 仅在单一吸引子区域训练，仍能准确预测未观测吸引子中的系统行为。
- 适用于复杂动态系统建模，尤其适合数据覆盖不全的场景。
机器学习方法可通过观测数据有效建模动态系统，但缺乏显式结构先验时，通常难以泛化到训练数据中表征不足的动态区域。本文证明，池化计算（Reservoir Computing, RC）这一简单、高效且通用的机器学习框架，在无显式结构先验的情况下，仍可泛化至未探索的状态空间。首先，我们提出一种多轨迹训练方案，支持在一系列不连续的时间序列上进行训练，从而更有效地利用现有数据。随后，将该方案应用于多稳态动态系统，结果表明：仅在单一吸引子区域训练的RC模型，能够捕捉完全未观测吸引子中的系统行为，实现域外泛化。
原文摘要 · Abstract (English)
Machine learning techniques offer an effective approach to modeling dynamical systems solely from observed data. However, without explicit structural priors -- built-in assumptions about the underlying dynamics -- these techniques typically struggle to generalize to aspects of the dynamics that are poorly represented in the training data. Here, we demonstrate that reservoir computing -- a simple, efficient, and versatile machine learning framework often used for data-driven modeling of dynamical systems -- can generalize to unexplored regions of state space without explicit structural priors. First, we describe a multiple-trajectory training scheme for reservoir computers that supports training across a collection of disjoint time series, enabling effective use of available training data. Then, applying this training scheme to multistable dynamical systems, we show that RCs trained on trajectories from a single basin of attraction can achieve out-of-domain generalization by capturing system behavior in entirely unobserved basins.
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