用深度学习捕捉时间序列的非线性动态，提升预测精度。
LETS Forecast: Learning Embedology for Time Series Forecasting
- 从时延嵌入中学习潜在空间，结合核回归建模动态
- 在噪声数据下仍保持稳定，优于当前最佳方法
- 适合需要高精度预测的复杂系统建模场景
真实世界的时间序列通常受复杂的非线性动力学支配。理解这些内在动态对精确未来预测至关重要。尽管深度学习在时间序列预测中取得重大进展，但许多现有方法并未显式建模动力学。为弥合这一差距，我们提出 DeepEDM 框架，将非线性动力系统建模与深度神经网络相结合。受经验动态建模（EDM）和 Takens 定理启发，DeepEDM 提出一种新型深度模型：从时延嵌入中学习潜在空间，并利用核回归近似底层动力学，同时采用高效的 softmax 注意力实现方式，支持对未来时间步的准确预测。我们在非线性动力系统合成数据以及跨领域的实际时间序列上进行了全面实验。结果表明，DeepEDM 对输入噪声具有鲁棒性，在预测准确性上优于当前最先进方法。代码已公开：https://abrarmajeedi.github.io/deep_edm。
原文摘要 · Abstract (English)
Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.
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