LETS 預測：學習嵌入學以進行時間序列預測

摘要

現實世界中的時間序列往往受到複雜的非線性動力學所支配。理解這些潛在的動力學對於精確預測未來至關重要。儘管深度學習在時間序列預測方面取得了重大成功，但許多現有方法並未明確地對這些動力學進行建模。為彌補這一差距，我們引入了DeepEDM，這是一個將非線性動力系統建模與深度神經網絡相結合的框架。受經驗動力建模（EDM）的啟發並基於Takens定理，DeepEDM提出了一種新穎的深度模型，該模型從時間延遲嵌入中學習潛在空間，並利用核回歸來近似底層動力學，同時利用softmax注意力的高效實現，從而實現對未來時間步的準確預測。為了評估我們的方法，我們在非線性動力系統的合成數據以及跨領域的現實世界時間序列上進行了全面的實驗。我們的結果表明，DeepEDM對輸入噪聲具有魯棒性，並且在預測準確性方面優於最先進的方法。我們的代碼可在以下網址獲取：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 預測：學習嵌入學以進行時間序列預測

LETS Forecast: Learning Embedology for Time Series Forecasting

摘要

Support