LETS Forecast: Learning Embedology for Time Series Forecasting

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.

Many real world time series, like stock prices, weather, or traffic, are shaped by complex systems with hidden variables. For example, while we can observe the price of a stock, we do not directly see the many interacting forces behind it, such as investor sentiment, global events, or economic signals. Most deep learning models try to predict future values by spotting patterns in the observed data, without understanding the system that generates it. Our method, DeepEDM, takes a different approach. Inspired by a technique called Empirical Dynamic Modeling, it reconstructs the hidden dynamics by using time delayed snapshots of the data and learning how the system evolves over time. By combining this with modern deep learning, DeepEDM makes accurate predictions even when the data is noisy or limited. It not only forecasts more reliably but also captures the underlying structure of the system, leading to better and more interpretable results on both synthetic and real world datasets.