LETS Forecast: Learning Embedology for Time Series Forecasting
Authors: name: Abrar Majeedi, name: Viswanatha Reddy Gajjala, name: Satya Sai Srinath Namburi GNVV, name: Nada Magdi Elkordi, name: Yin Li

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.