A physics-informed hybrid neural network for interpretable and accurate fish growth prediction in recirculating aquaculture systems

• A novel hybrid model integrates LSTM and PINN for robust fish growth prediction in RAS. • The architecture explicitly embeds biophysical constraints within a differential-algebraic framework. • Hierarchical LSTM captures dependencies between water quality parameters, feeding amount, and historical growth data. • Deployment on a RAS platform demonstrates feasibility for intelligent aquaculture management and digital twin development. Fish growth prediction in recirculating aquaculture systems (RAS) is significantly affected by various factors, including water temperature, dissolved oxygen levels, pH, and feeding amounts. This study proposes a long short term memory physics informed gated recurrent unit (L-PIGRU) model to correlate the fish growth with water quality and feeding amounts, in which (1) the long short-term memory (LSTM) module maps environmental factors to physical states and captures long-range nonlinear coupling effects through a hierarchical structure; (2) the physics informed gated recurrent unit (PIGRU) framework integrates temporal modeling with biophysical constraints using a differential–algebraic formalism, enabling precise characterization of nonlinear aquaculture dynamics. L-PIGRU integrates empirical data with constraints derived from biophysical equations, leveraging the predictive power of data-driven methods to model complex phenomena while ensuring model interpretability. This approach enhances both the flexibility and rationality of the model. Furthermore, the proposed model was verified through deployment on a RAS platform, where rigorous experimental procedures were conducted within a controlled environment. The validation results demonstrate that L-PIGRU achieves satisfactory accuracy, with a root mean square error of 2.39, a mean absolute error of 2.09, and a mean absolute percentage error of 0.68%. Finally, Lyapunov theory was employed to analyze the convergence of the prediction model, ensuring the robustness of the forecast results. By balancing physical constraints with data-driven approaches, L-PIGRU serves as a high-accuracy, interpretable predictive tool for fish growth analysis, offering valuable support for intelligent aquaculture management.