Physics-Informed Machine Learning with Monotonic Constraints for Daily Fuel Consumption and CII Prediction of Ships

As the annual reduction factors of the International Maritime Organization (IMO) Carbon Intensity Indicator (CII) regulation have progressively tightened, predicting ship fuel consumption from operating conditions before a voyage has become essential. However, existing data-driven predictors suffer from two methodological blind spots: the possibility of non-physical responses and the optimism bias of random validation splits. This study proposes a physics-informed machine learning framework for predicting the total daily fuel consumption of a ship (propulsion, hotel, and auxiliary loads together), in which the physical requirement that, at a given speed, fuel consumption must not decrease as weather worsens (partial monotonicity) is imposed on Random Forest and XGBoost models as explicit monotonic constraints. The framework is coupled with a CII computation engine reflecting the IMO MEPC resolutions and validated under a protocol that prevents information leakage in operational time series: validation on contiguous time blocks with buffer zones, rotated across repetitions; cross-validation folds that follow the same time-block rule (split-consistent out-of-fold (OOF) prediction); and an audit removing input variables from which the target is arithmetically derivable. The framework is dataset-agnostic; its empirical validation is reported for the measured data that are openly available. On measured data from three ships of different types, sizes, and propulsion systems, the constrained XGBoost achieved R2 = 0.943 ± 0.007 with no accuracy loss (ΔR2 = +0.006) while completely eliminating non-physical reversals in the accumulated local effects (8, 7, and 9 → 0). The optimism bias of random splitting was quantified as +0.032, a systematic difference relative to seed-level dispersion, and a ship fixed-effects regression showed that the speed elasticity of fuel consumption—the exponent of the speed–fuel power law—is not identifiable from annual public aggregates. When the predicted fuel consumption was converted to a CII, the mean absolute percentage error was 6.80%, and the predicted rating agreed with the measured rating in 80.6% of the records (95.8% within one grade). Within the scope of the three validated ships, these results indicate that the framework can serve as a pre-voyage screening tool for CII planning; validation on mainstream cargo ships remains to be done.