Data-driven modelling is essential in aquaculture, especially for complex systems where internal environmental conditions and reaction mechanisms are difficult to describe accurately. However, the black-box nature and high data dependency of traditional data-driven models limit their practical applicability. To address these challenges, we propose a physics-informed spatial self-attention gated recurrent (PSAG) unit model that integrates process data with domain-specific physical constraints. The spatial self-attention (SSA) module extracts key features from the process data through convolutional operations weighted by attention scores, which are then passed to the gated recurrent unit (GRU) for spatial prediction. The model was validated using data from an aquaculture biofilter system. Results showed that the spatial self-attention GRU framework performs well under conditions of limited data and significant distribution shifts, and that the inclusion of physical constraints could further improve predictive accuracy.