LETS预测：面向时间序列预测的嵌入学习框架

摘要

现实世界中的时间序列往往受复杂的非线性动力学支配。理解这些潜在的动力学机制对于精确预测未来至关重要。尽管深度学习在时间序列预测领域已取得重大成功，但许多现有方法并未明确建模这些动力学特性。为弥合这一差距，我们提出了DeepEDM框架，该框架将非线性动力学系统建模与深度神经网络相结合。受经验动力学建模（EDM）启发并基于Takens定理，DeepEDM提出了一种新颖的深度模型，该模型从时间延迟嵌入中学习潜在空间，并采用核回归来近似底层动力学，同时利用softmax注意力的高效实现，从而实现对未来时间步长的准确预测。为评估我们的方法，我们在非线性动力学系统的合成数据以及跨领域的真实世界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，并在预测准确性上超越了现有最先进的方法。我们的代码可在以下网址获取：https://abrarmajeedi.github.io/deep_edm。

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.

LETS预测：面向时间序列预测的嵌入学习框架

LETS Forecast: Learning Embedology for Time Series Forecasting

摘要

Support