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

TL;DR

EgPDE-Net is a novel continuous-time neural network model that learns unknown PDE systems in multivariate time series, effectively incorporating exogenous variables and enabling arbitrary-step prediction with improved accuracy.

Contribution

The paper introduces EgPDE-Net, a new PDE-based neural network that models multivariate time series with exogenous variables, allowing for flexible future predictions and improved performance.

Findings

Achieves 9.85% lower RMSE than baselines

Reduces 13.98% MAE compared to existing methods

Effective in modeling complex exogenous influences

Abstract

While exogenous variables have a major impact on performance improvement in time series analysis, inter-series correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of multivariate time series could be modelled with complex unknown partial differential equations (PDEs) which play a prominent role in many disciplines of science and engineering. In this paper, we propose a continuous-time model for arbitrary-step prediction to learn an unknown PDE system in multivariate time series whose governing equations are parameterised by self-attention and gated recurrent neural networks. The proposed model, \underline{E}xogenous-\underline{g}uided \underline{P}artial \underline{D}ifferential \underline{E}quation Network (EgPDE-Net), takes account of the relationships among the exogenous variables and their effects on the target series. Importantly, the model can be reduced into a regularised ordinary differential equation (ODE) problem with special designed regularisation guidance, which makes the PDE problem tractable to obtain numerical solutions and feasible to predict multiple future values of the target series at arbitrary time points. Extensive experiments demonstrate that our proposed model could achieve competitive accuracy over strong baselines: on average, it outperforms the best baseline by reducing $9.85\%$ on RMSE and $13.98\%$ on MAE for arbitrary-step prediction.