Hybrid LSTM-heat transfer equation model for key parameter prediction in process industry

Abstract Accurate prediction of temperature and energy consumption in process industries faces challenges from noisy sensor data and physical model parameter sensitivity. This paper proposes a hybrid model combining Long Short-Term Memory (LSTM) networks with the heat transfer equation to balance data-driven flexibility and physical interpretability. The LSTM captures nonlinear temporal features from multi-sensor data (temperature, flow rate, pressure), while the heat transfer equation provides physical constraints through discretized thermal diffusion simulations. An attention mechanism dynamically weights the outputs of both channels, and a joint loss function enforces both data accuracy and physical consistency. Experiments on a real-world dataset from a magnesia production plant (10, 000+ time steps) demonstrate that the hybrid model reduces RMSE by 32% (from 2.17°C to 1.48°C) compared to pure LSTM and 61% compared to the pure physical model. The results highlight the model’s ability to handle sensor noise while adhering to thermodynamic laws.