Fast and accurate resistance prediction is critical in early-stage ship design. While Michell’s thin-ship theory provides rapid evaluations, its linear assumptions limit accuracy, particularly as hull forms deviate from ideal slenderness. This paper introduces a physics-preserving neural calibration method that improves Michell’s theory without replacing the underlying solver. We train a two-dimensional convolutional encoder–decoder, conditioned on Froude numbers via global FiLM modulation, to predict a bounded correction to the geometric effective-slope field. Because the solver remains unchanged, the learned correction acts as an interpretable spatial perturbation rather than a black-box resistance map. Evaluated under a strict leave-one-family-out (LOFO) protocol on a fleet of five slender hull families (DTMB, NPL-4A, Wide-Light Canoe, Wigley, and Delft 372), the neural calibration achieves a mean absolute percentage error (MAPE) of 0.0741. This represents a 24% improvement over a reproduced 2020 baseline and a 7.9% improvement over the uncorrected Michell solver. The 2020 baseline is the rigid boundary-layer and phase-deflection correction of an earlier study by the present group, re-evaluated here on the present hulls at their measured attitudes. Ablation studies show that much of this aggregate gain is captured by a bounded global slope offset, indicating that a spatially uniform displacement correction accounts for most of the improvement on slender hulls, while the spatially varying field mainly adds per-family headroom. Finally, we map the physical boundaries of this approach. Dedicated recovery campaigns on fuller forms (KCS and Series 60) show that the model regresses compared to baselines. This confirms that while the correction successfully refines the linear source distribution for slender hulls, it cannot synthesize missing physics, such as stagnation pressure, separated flow, or wave interference, for fuller or unrelated geometries.

A boundary-condition closure is presented for renormalised, least-squares corrected meshless Laplacian operators in strong-form collocation on point clouds.Unlike the dominant particle-based treatments, the closure does not pad the domain with auxiliary particles, represent the boundary with a level set, or enforce the conditions weakly.A single code path folds Neumann, Dirichlet, and Robin conditions directly into the discrete collocation row, organised by condition type, so that a prescribed flux enters the right-hand side while a value-dependent condition contributes to the diagonal.The Neumann flux is imposed through a tangential projection in physical space before renormalisation, and a general Gram projector treats non-orthogonal corners exactly.A complementary algebraic-ghost closure completes the truncated boundary stencil by reflecting the local support across the nearby boundary planes, requiring no extra unknowns.The free surface is detected from the support-deficiency geometry of the cloud, and its enforcement strength reduces exactly to the total kernel weight, so no penalty coefficients or case-dependent thresholds are introduced.The resulting method, named FIRM (Flux-Integrated Renormalised Meshless), is verified in two dimensions against analytical solutions and irregular-domain Poisson benchmarks, on regular and highly irregular point clouds, alongside a second-order generalised finite difference baseline.The value closure exhibits supraconvergence, the algebraic-ghost closure reduces the Neumann-limited error by about an order of magnitude, and with the sum normalisation the method approaches second-order convergence at straight boundaries.The renormalised operators are also consistent for a single Helmholtz--Hodge decomposition, whose residual divergence equals the composition defect of the operators and vanishes under refinement.

The maritime industry faces increasing pressure to improve energy efficiency, a challenge that extends to the luxury yacht sector. This study presents a comprehensive hydrodynamic assessment for retrofitting a bespoke Energy Saving Device (ESD) onto a 45 m motor yacht. A full-scale self-propulsion Computational Fluid Dynamics (CFD) model was developed and validated directly against dedicated sea trial data, ensuring high fidelity and bypassing traditional scaling uncertainties. The validated model was then utilized to design and optimize a custom pre-propeller duct system. A parametric study varying the duct’s angle of attack identified an optimal configuration of ${20}^{\circ }$, which achieves a definitive power saving of 4.7% at the vessel’s cruise speed of 12.3 knots. Analysis of the propulsive factors reveals that the gain is primarily driven by a substantial increase in the hull efficiency, ${\eta }_H$, achieved by conditioning the propeller inflow. This improvement successfully compensates for the corresponding decrease in the propeller’s open-water efficiency, ${\eta }_o$. This work demonstrates a successful end-to-end numerical workflow for designing and verifying an effective, retrofittable ESD, highlighting a practical solution for reducing fuel consumption in existing motor yachts.