Origin of the Estimated Departure from the Engineering Physics

Determine whether the unrestricted structural regression’s preference for a falling engine-efficiency curve reflects how ship fuel consumption is reported or a genuine departure of fuel consumption from the engineering physics underlying the calibrated maritime emissions model.

Background

The paper compares engineering-calibrated models with unrestricted structural regressions that estimate the coefficients of the engine-efficiency curve from reported annual fuel consumption. For dry bulk and container ships, the unrestricted regression favors a falling efficiency curve over the calibrated curve, producing an attenuated and differently shaped response of fuel consumption to sailing speed. A design-load restriction restores a response closer to the engineering benchmark, but the restriction does so by removing the flexibility through which the flat response arises rather than by demonstrating that the calibrated curve is correct.

The authors explicitly state that the available data cannot distinguish whether the estimated preference is caused by reporting features or represents a real physical departure from the engineering model. Resolving this issue would clarify whether the apparent attenuation of the speed response reflects measurement or reporting processes, or instead indicates that the conventional engineering relationship is misspecified.

References

Whether that preference reflects how consumption is reported or a real departure from the physics, these data cannot say.

— Modeling Shipping Emissions: Machine Learning, Engineering, and Policy Counterfactuals  (2610.01008 - Kasahara et al., 1 Oct 2026) in Section 5.3, “Nonlinearity” (Performance Explanation)