arXiv:2510.04342cs.LG2025-10

按复杂度渐进训练,让模型更准预测混沌系统。

Learning to Predict Chaos: Curriculum-Driven Training for Robust Forecasting of Chaotic Dynamics

  • 从周期性到混沌系统,按动态理论分阶训练
  • 预测时长比随机训练多40%,比纯真实数据训练翻倍
  • 适配多种模型,对科学预测和医疗信号有用

预测混沌系统是众多科学领域的核心挑战,因微小误差会指数放大。当前机器学习方法常陷入两个困境:过度专注单一系统(如Lorenz-63),导致泛化能力差;或混杂大量无关时间序列,难以掌握特定动力学特征。本文提出课程式混沌预测(CCF)训练范式,基于动力系统理论组织训练数据,按复杂度从简单周期行为逐步过渡到高度混沌动态。复杂度以最大李雅普诺夫指数和吸引子维数量化。通过先在可预测系统上训练,再逐步引入更复杂的轨迹,模型得以构建稳健且通用的动力学表征。我们构建了超过50个合成常微分/偏微分方程系统构成课程库。实验表明,采用CCF预训练显著提升在未见真实世界基准上的表现:在太阳黑子、电力需求和人类心电图数据集上,预测有效时长远超随机训练(最多延长40%),且超过仅用真实数据训练的两倍以上。该优势在GRU、Transformer等多种神经架构中一致存在,并通过详尽消融实验证实课程结构的关键作用。

原文摘要 · Abstract (English)

Forecasting chaotic systems is a cornerstone challenge in many scientific fields, complicated by the exponential amplification of even infinitesimal prediction errors. Modern machine learning approaches often falter due to two opposing pitfalls: over-specializing on a single, well-known chaotic system (e.g., Lorenz-63), which limits generalizability, or indiscriminately mixing vast, unrelated time-series, which prevents the model from learning the nuances of any specific dynamical regime. We propose Curriculum Chaos Forecasting (CCF), a training paradigm that bridges this gap. CCF organizes training data based on fundamental principles of dynamical systems theory, creating a curriculum that progresses from simple, periodic behaviors to highly complex, chaotic dynamics. We quantify complexity using the largest Lyapunov exponent and attractor dimension, two well-established metrics of chaos. By first training a sequence model on predictable systems and gradually introducing more chaotic trajectories, CCF enables the model to build a robust and generalizable representation of dynamical behaviors. We curate a library of over 50 synthetic ODE/PDE systems to build this curriculum. Our experiments show that pre-training with CCF significantly enhances performance on unseen, real-world benchmarks. On datasets including Sunspot numbers, electricity demand, and human ECG signals, CCF extends the valid prediction horizon by up to 40% compared to random-order training and more than doubles it compared to training on real-world data alone. We demonstrate that this benefit is consistent across various neural architectures (GRU, Transformer) and provide extensive ablations to validate the importance of the curriculum's structure.

混沌预测课程学习时间序列动力系统

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