LETS Forecast: Learning Embedology for Time Series Forecasting

TL;DR

DeepEDM combines nonlinear dynamical systems modeling with deep neural networks to improve time series forecasting accuracy, especially in complex real-world scenarios.

Contribution

The paper introduces DeepEDM, a novel framework that integrates empirical dynamic modeling with deep learning for better time series prediction.

Findings

DeepEDM outperforms state-of-the-art methods in forecasting accuracy.

DeepEDM is robust to input noise.

DeepEDM effectively models complex nonlinear dynamics.

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.