EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction With Exogenous Variables

Area of Science:

• Time Series Analysis
• Dynamical Systems Modeling
• Machine Learning for Scientific Computing

Background:

• Exogenous variables significantly impact time series forecasting, but their interseries correlation and time dependence are often overlooked in current continuous-time models.
• Multivariate time series dynamics are frequently governed by complex, unknown partial differential equations (PDEs), crucial in various scientific and engineering fields.

Purpose of the Study:

• To propose a novel continuous-time model capable of learning unknown partial differential equation (PDE) systems within multivariate time series.
• To effectively incorporate the influence of exogenous variables on target series prediction using a unified framework.

Main Methods:

• Introduced the exogenous-guided PDE network (EgPDE-Net), a continuous-time model parameterizing PDE governing equations with self-attention and gated recurrent neural networks.
• Developed a regularization strategy enabling the reduction of the PDE problem to a tractable, regularized ordinary differential equation (ODE) problem for numerical solutions.
• Enabled arbitrary-step prediction for multiple future values at any time points.

Main Results:

• The proposed EgPDE-Net effectively models relationships among exogenous variables and their impact on target series.
• The model achieved competitive accuracy, outperforming strong baselines by reducing Root Mean Square Error (RMSE) by 9.85% and Mean Absolute Error (MAE) by 13.98% on average for arbitrary-step predictions.

Conclusions:

• The EgPDE-Net provides a robust and accurate method for learning unknown PDE systems in multivariate time series, considering exogenous variable dynamics.
• The model's ability to handle arbitrary-step prediction and its superior performance demonstrate its potential for advancing time series forecasting in complex scientific domains.