A Stacking Ensemble Model of VAR, Dynamical System, and LSTM for Bivariate Forecasting of Humidity and Temperature in a Melon Greenhouse

This study proposes an ensemble model that combines the Vector Autoregression (VAR) approach, a dynamic system based on Ordinary Differential Equations (ODE), and Long Short-Term Memory (LSTM) for bivariate forecasting of temperature and humidity in a melon greenhouse. The VAR model captures linear relationships between variables, the dynamic system models nonlinear relationships based on physical parameters, and the LSTM handles complex nonlinear patterns. The forecasts from the three models are combined using a stacking ensemble model. Model evaluation was conducted using RMSE, MAE, and SMAPE metrics. The results show that the stacking ensemble model produces more accurate and stable predictions compared to individual models. The ensemble model achieved the lowest error values across all metrics: RMSE of $\mathbf{1. 3 9}$, MAE of $\mathbf{1. 0 9 \%}$, MAPE of $\mathbf{2. 1 2 \%}$, and SMAPE of $\mathbf{2. 1 2 \%}$.