A dual-physical-constraint modeling framework for ship fuel consumption prediction

To advance energy-efficient operations in the shipping industry, high-precision prediction of ship fuel consumption is crucial for optimizing voyage planning. Existing data-driven fuel consumption prediction models generally exhibit insufficient generalization ability and poor prediction stability, thus failing to satisfy the practical requirements of voyage fuel consumption prediction. To address these issues, this study proposes a dual-constrained adaptive physics-informed neural network (DA-PINN) modeling framework. The proposed framework incorporates two types of physical prior knowledge as constraints: boundary physical constraints derived from the structural boundaries of physical mechanistic models, and trend physical constraints reflecting statistical patterns observed in historical data. Corresponding physical constraint loss terms are calculated based on the deviations between the model's predictions and the two types of prior knowledge. By adaptively adjusting the weights of the data fitting loss and the two physical constraint loss terms during the deep neural network training, the framework achieves a dynamic trade-off between prediction accuracy and physical consistency. This study validates the proposed framework using multiple sets of measured data from the ballast and full load voyages of large tankers. The results demonstrate that the DA-PINN model exhibits superior extrapolation stability and reliability. Compared to traditional black-box models, the DA-PINN achieves significant improvements in key performance indicators: MAE is reduced by 17.71 %, MAPE by 17.78 %, RMSE by 17.29 %, and R2 is increased by 11.49 %. The proposed DA-PINN framework provides an effective solution for enhancing the practicality and credibility of data-driven models in complex shipping scenarios.