用递归网络加迁移学习，预测混沌系统长期统计特性变化
Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning
- 用回声状态网络结合迁移学习，捕捉参数变化下的混沌吸引子演化
- 在不同参数下预测轨迹准确时间显著延长，且能反映长期统计规律改变
- 适合研究复杂非线性系统的科学家，尤其关注长期行为建模的场景
本文研究回声状态网络（ESN）对广义库拉莫托-希瓦辛斯基（gKS）方程的预测能力，该方程是典型的具有时空混沌特性的非线性偏微分方程。研究重点在于预测当色散关系或空间域长度变化时，gKS模型长期统计模式的演变。通过迁移学习，我们将ESN适配到不同参数设置，并成功捕捉了底层混沌吸引子的变化。以往工作表明，迁移学习可有效用于ESN的单轨预测；本工作的创新在于将此方法拓展至预测时空混沌偏微分方程的长期统计特性。此外，我们还证明迁移学习显著提升了单个gKS轨道预测的准确性持续时间。
原文摘要 · Abstract (English)
In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibits spatiotemporal chaos. Our research focuses on predicting changes in long-term statistical patterns of the gKS model that result from varying the dispersion relation or the length of the spatial domain. We use transfer learning to adapt ESNs to different parameter settings and successfully capture changes in the underlying chaotic attractor. Previous work has shown that transfer learning can be used effectively with ESNs for single-orbit prediction. The novelty of our paper lies in our use of this pairing to predict the long-term statistical properties of spatiotemporally chaotic PDEs. We also show that transfer learning nontrivially improves the length of time that predictions of individual gKS trajectories remain accurate.
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