EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction with Exogenous Variables
This work addresses time series forecasting for domains like science and engineering by incorporating exogenous variable relationships, though it is incremental as it builds on existing continuous methods.
The paper tackles the problem of multivariate time series prediction with exogenous variables by proposing EgPDE-Net, a continuous-time model that learns unknown PDE systems using self-attention and gated RNNs, achieving an average reduction of 9.85% in RMSE and 13.98% in MAE over baselines for arbitrary-step prediction.
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.