A hybrid physics-informed gated recurrent unit framework for robust temperature forecasting in greenhouse aquaponic systems

• A physics-informed framework integrates energy balance equations for temperature forecasting. • Neural architecture comparison reveals an optimized design for greenhouse forecasting. • Model adapts across three aquaponic systems under varied temporal-spatial conditions. • Greenhouse characteristics influence forecasting performance across different facilities. Accurate temperature forecasting is vital for greenhouse aquaponic systems (GAPS), yet purely data-driven models often fail under non-stationary operational conditions. This paper proposes a hybrid Physics-Informed Gated Recurrent Unit (PIGRU) framework that integrates greenhouse energy balance principles directly into the recurrent neural network architecture. The key innovation lies in embedding a DOPRI5-based numerical solver within the training loop to reconcile neural network outputs with thermodynamic differential equations. Experimental results across three independent greenhouse facilities demonstrate that the proposed model achieves superior robustness, with an R 2 of 0.91 in cross-facility extrapolation scenarios, significantly outperforming baseline GRU models. Under extreme fluctuations, the model maintains stable performance while pure data-driven baselines show substantial degradation. This approach provides a reliable tool for precision control in complex agricultural environments.