Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle to learn the dynamics unless key information about the underlying system is already known. We focus on the important problem of basin prediction -- determining which attractor a system will converge to from its initial conditions. First, we show that the predictions of standard RC models (echo state networks) depend critically on warm-up time, requiring a warm-up trajectory containing almost the entire transient in order to identify the correct attractor even after being trained with optimal hyperparameters. Accordingly, we turn to Next-Generation Reservoir Computing (NGRC), an attractive variant of RC that requires negligible warm-up time. By incorporating the exact nonlinearities in the original equations, we show that NGRC can accurately reconstruct intricate and high-dimensional basins of attraction, even with sparse training data (e.g., a single transient trajectory). Yet, a tiny uncertainty on the exact nonlinearity can already break NGRC, rendering the prediction accuracy no better than chance. Our results highlight the challenges faced by data-driven methods in learning the dynamics of multistable systems and suggest potential avenues to make these approaches more robust.

翻译：储层计算（Reservoir Computing，RC）是一种简单高效的无模型框架，用于根据数据预测非线性动力系统的行为。本文表明，对于某些常见研究系统，除非已获知底层系统的关键信息，否则主流RC框架难以学习其动力学特性。我们聚焦于盆地预测这一重要问题——即判定系统从初始状态收敛至哪个吸引子。首先发现，标准RC模型（回声状态网络）的预测精度严重依赖于预热时间：即使采用最优超参数训练，仍需包含几乎整个瞬态过程的预热轨迹才能确定正确吸引子。为此，我们转向下一代储层计算（Next-Generation Reservoir Computing，NGRC）——这种具有吸引力的RC变体所需预热时间可忽略不计。通过精确纳入原始方程中的非线性项，NGRC能准确重建复杂高维吸引盆，甚至在稀疏训练数据（如单次瞬态轨迹）条件下也能实现。然而，非线性项中微小的不确定性即可导致NGRC失效，使其预测精度与随机猜测无异。本研究揭示了数据驱动方法在学习多稳态系统动力学时面临的挑战，并为增强这些方法的鲁棒性提供了潜在方向。