LETS Forecast: Learning Embedology for Time Series Forecasting

2025-06-06

AI Summary

Real-world time series are often governed by complex nonlinear dynamics, yet most existing deep learning approaches neglect explicit modeling of such underlying dynamical systems. To address this, we propose DeepEDM—a differentiable and scalable framework that tightly integrates Takens’ delay embedding theory with deep neural networks. DeepEDM jointly leverages dynamic-aware latent space construction, empirical dynamic modeling (EDM), kernel regression, and soft attention mechanisms to capture system evolution for high-accuracy long-term forecasting. Evaluated on diverse chaotic synthetic benchmarks and cross-domain real-world sequences—including meteorological, traffic, and energy time series—DeepEDM consistently outperforms state-of-the-art methods. It demonstrates superior robustness to strong noise and exceptional long-term stability. By systematically incorporating dynamical-systems priors into deep time-series modeling, DeepEDM establishes a novel paradigm for physics-informed, interpretable, and generalizable sequence prediction.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Modeling complex nonlinear dynamics in time series
• Integrating dynamical systems with deep neural networks
• Improving forecasting accuracy using latent embeddings

Innovation

• Integrates dynamical systems with deep networks
• Learns latent space from time-delayed embeddings
• Uses kernel regression for dynamics approximation