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Localized Generative Design of Ship Hulls with Diffusion Models and High-Fidelity Assessment

Hadi Keramati, Mohammed A. Hannan, Patrick Kirchen, Sina Tousi, Joonas Riekkinen, Jim Pyra, Rajeev K. Jaiman

arXiv:2610.12870v1math.APcs.AImath-ph

TL;DR

Localized hull design must reduce resistance while preserving vessel requirements, although bow modifications can have speed-dependent effects and high-fidelity CFD is costly. The paper uses masked, reward-directed diffusion and an automated CFD pipeline to assess generated and expert-refined hulls. The CFD comparisons reveal speed-dependent resistance tradeoffs and limitations in the representation and reward.

  • Problem

    Localized hull optimization must reduce resistance while retaining vessel requirements, and bow modifications can have different effects across operating conditions.

    Source: §1 · p. 2

  • Method

    The framework uses parametric masking and surrogate-guided reward-directed SMC to generate localized KCS hull variants, then assesses selected hulls with automated viscous CFD.

    Source: §1 · p. 4, §5 · p. 24

  • Results

    Model 1 had comparable total resistance to KCS at Fn = 0.195 but 45–50% higher at Fn = 0.250 and 0.260; GenHull E was 6–8% lower up to Fn = 0.240, then higher above Fn = 0.250.

    Source: §5 · p. 24

  • Takeaways & Limitations

    Matching integral form coefficients and passing feasibility checks do not establish hydrodynamic performance or preserve stability margins; richer geometry and reward fidelity are needed.

    Source: §5 · p. 25

    The framework’s reward lacks viscous-pressure and stability terms, and its geometric parameterization requires greater fidelity to represent useful features.

    Source: §4.3 · p. 22, §4.4 · p. 24, §5 · p. 25

Abstract

from arXiv · show

Practical ship design requires localized refinement and performance evaluation. This paper presents a reward-directed diffusion framework for localized hull optimization. Parametric masking during dataset generation restricts geometric changes to selected variables, including the bulbous bow and forebody, while preserving full-hull continuity. Surrogate-assisted sequential Monte Carlo sampling targets reduced predicted calm-water resistance, with stability retained through training data and displacement matched during screening. An automated viscous free-surface CFD pipeline, validated against measurements for two benchmark container ships, evaluates a generated variant and GenHull E, a hull refined by a naval architect within the same representation. At matched KRISO Container Ship (KCS) displacement, the generated variant has comparable total resistance at $F_n=0.195$ but 45-50% higher resistance at $F_n=0.250$ and $0.260$, missed by empirical screening. GenHull E achieves 6-8% lower total resistance up to $F_n=0.240$ but higher resistance above $F_n=0.250$ as opposing friction and pressure trends reverse the gains. Aggregating resistance across this crossover can conceal tradeoffs that emerge when friction and pressure components are evaluated separately. The assessment reveals an inability to represent a faired bulbous bow and a reward lacking viscous pressure and stability terms. These findings show how high-fidelity assessment informs improved representations and objectives for physically realizable generative designs.

1. Introduction

Localized hull optimization must balance resistance reduction with vessel constraints and geometric continuity, while accounting for speed-dependent effects and the cost of high-fidelity assessment. The paper introduces a masked, reward-directed diffusion framework for KCS and assesses generated and expert-refined hulls with an automated CFD pipeline.

1. Introduction

  • Hull optimization must reduce resistance while retaining displacement, carrying capacity, and operational characteristics, often by modifying selected features of an established parent hull.Localized changes require flexible parameterization, controlled extent, and smooth transitions to retained surfaces.Source: §1 · p. 2
  • Bulbous-bow and forebody changes can help at one speed or draft but become less beneficial or detrimental at another, while repeated viscous free-surface CFD is computationally expensive.Semi-empirical methods offer rapid estimates but may not resolve hydrodynamic effects of localized geometry changes.Source: §1 · p. 2
  • Surrogates make candidate screening cheaper, but their predictions require verification and depend on training-data coverage, operating conditions, and candidate distance from evaluated designs.Reduced design spaces and physically meaningful shape variations also influence optimization efficiency.Source: §1 · pp. 2–3
  • Generative models learn hull-geometry relationships, but sampling must be directed toward performance objectives while satisfying relevant constraints.Reward-directed diffusion can use derivative-free value guidance and sequential Monte Carlo to resample promising trajectories without retraining the denoising model.Source: §1 · p. 3
  • The proposed KCS framework masks geometric changes to the bulbous bow and forebody, uses surrogate-guided SMC for lower predicted resistance, and assesses a sampled variant and an expert-refined hull with automated CFD.The pipeline is validated against KCS and Duisburg Test Case benchmarks; the assessment exposes limitations in representation, reward fidelity, operating-range aggregation, and stability-margin preservation.Source: §1 · pp. 3–4

2. Methodology

The methodology combines localized hull-form generation with surrogate-guided sampling and automated CFD assessment. Its validation supports comparative hull ranking under matched conditions, while bounding what the CFD comparisons can establish.

2. Methodology

  • Fourteen bow and bulbous-bow variables vary while other variables remain at baseline KCS values; 3,800 LHS designs meeting stability constraints train the resistance surrogate.Surrogate labels use Michell’s integral for wave-making resistance and the ITTC-57 correlation line for frictional resistance.Source: §2 · p. 4

2.1. DDPM Formulation

  • The DDPM learns from full design vectors whose dataset-level masking concentrates variation in the bow while preserving a full-hull representation.Standard reverse diffusion samples from the learned data distribution without performance preference, motivating reward guidance.Source: §2 · p. 4, §2.1 · p. 6

2.2. Sequential Monte Carlo sampling

  • SMC uses the ResNet surrogate to reward lower predicted drag, with exponential tilting and a temperature parameter guiding reverse diffusion while retaining diversity.Resampling is triggered when effective sample size falls below 0.5N to mitigate weight degeneracy and particle collapse.Source: §2.2 · p. 6

2.3. CFD Evaluation of Resistance

  • The automated CFD pipeline derives mesh and solver settings from hull geometry and Froude number, applying the same rules to compared hulls.Cases use fixed even keel and prescribed draft, unlike free-sink/trim experiments; at Fn = 0.260, measured-attitude reruns raised total resistance by 0.88% and skin friction by 1.9%.Source: §2.3 · pp. 8–9

2.3.1. Validation Against Benchmark Hulls

  • KCS total-resistance errors ranged from +14.0% to −8.9% overall and +6.7% to −3.1% over Fn = 0.152–0.227; DTC errors ranged from −4.1% to −7.5%.Both benchmarks were evaluated at six Froude numbers using the automated pipeline.Source: §2.3.1 · pp. 9, 11, Table 3 · p. 10, Table 4 · p. 10
  • The validation errors form a bounded envelope with identified mesh-resolution causes, but viscous resistance did not converge under refinement and total-resistance GCI was not established.The pipeline is suited to comparative ranking at matched Froude number, not absolute resistance prediction; cancellation between dissimilar hull forms cannot be assumed.Source: §2.3.1 · pp. 11–12

3. Results

The results compare diffusion and sampling diagnostics, empirical screening, and viscous CFD assessments of a generated variant and GenHull E. The high-fidelity comparisons reveal speed-dependent resistance tradeoffs and limitations in the hull representation and numerical assessment.

3.1. Diffusion Accuracy and Sampling Diversity

  • The diffusion diagnostics assess held-out noise-prediction error and reverse-step posterior KL divergence, while the sampler tracks normalized ESS and resamples when ESS/N < 0.5.The figure captions define the plotted measures and clarify that ESS is evaluated before resampling.Source: §3.1 · pp. 12, 14, Figure 5 · p. 13, Figure 6 · p. 14

3.2. Screening and CFD Assessment of Generated Hull Forms

  • At matched KCS displacement, Model 1’s total resistance was −1.2% at Fn = 0.195 but 44.9% and 49.3% higher at Fn = 0.250 and 0.260, respectively.The empirical screening did not capture the increase near the design speed; it used an empirical regression and resistance aggregated across a wide Froude range.Source: §3.2 · p. 15

3.3.1. Geometry and Hydrostatics

  • GenHull E has no bulbous bow because the representation cannot express a faired bulb; at matched length, draft, and displacement, it has 6.97% less wetted surface and 6.96% greater beam than KCS.Its waterplane inertia is 12.46% lower and its transverse metacentric radius BMT is 12.93% lower; at KG = 13.0 m, its maximum righting lever is 1.39 m at 37.5°, versus 1.11 m at 30° for KCS.Source: §3.3 · p. 15, §3.3.1 · pp. 16–17, Figure 7 · p. 16

3.3.2. Resistance Comparison with KCS

  • GenHull E had 6–8% lower total resistance than KCS from Fn = 0.152 to 0.240, then higher resistance above that range, with the crossover at Fn = 0.250.At the crossover the difference was +0.61%, or 0.43 N on 70 N, and was indistinguishable from zero; the four successive averaging windows located it at Fn = 0.250 within method repeatability.Source: §3.3.2 · pp. 18–19, Table 6 · p. 18, Figure 9 · p. 18
  • GenHull E’s friction difference from KCS remains negative as speed increases, while its pressure difference rises sharply above Fn = 0.240 and overtakes the friction advantage.The pressure difference reaches 8.5, 14.0, and 21.4 N at Fn = 0.250, 0.260, and 0.270, respectively; Figure 9 reports total resistance and the pressure and friction components.Source: Table 6 · p. 18, Figure 9 · p. 18, §3.3.2 · p. 19

3.3.3. Free-Surface and Hull Pressure Fields

  • At Fn = 0.270, GenHull E has a stronger free-surface wave system than KCS, while its forebody develops stronger suction without the bulb’s canceling wave system.The pressure-field comparison is shown on the wetted forebody at Fn = 0.227 and 0.270.Source: §3.3.3 · pp. 19, 21, Figure 10 · p. 19, Figure 11 · p. 20

3.3.4. Limitations of the Comparison

  • GenHull E’s lower boundary-layer coverage may favor its measured resistance advantage by approximately 1.4% of total resistance, a discretization contribution the authors say should be discounted.The meshes do not permit physical and numerical contributions to the remaining discrepancy to be distinguished, and no correction was applied; no GenHull E grid-convergence study was performed.Source: §3.3.4 · p. 21

4. Discussion

Resistance comparisons reverse with operating speed, while the discussion identifies limitations in bulb geometry, stability treatment, and the empirical reward. These findings motivate speed-resolved, higher-fidelity evaluation and a richer geometric representation.

4.1. Influence of Froude Number on the Resistance Comparison

  • GenHull E shifts from 8.4% lower total resistance than KCS at Fn = 0.195 to 13.7% higher at Fn = 0.270; Model 1 is 45–50% higher at Fn = 0.250 and 0.260.Model 1 was comparable to KCS at Fn = 0.195, despite empirical screening predicting a lower resistance coefficient near Fn = 0.26.Source: §4.1 · p. 21
  • Above Fn = 0.240, GenHull E’s wave-making penalty grows faster than its friction advantage, and seven paired computations were needed to bracket the crossover.The friction advantage grows smoothly with dynamic pressure; averaging across the reversal can conceal performance at individual speeds.Source: §4.1 · pp. 21–22
  • The reward spans Fn = 0.10 to 0.45, but its high-speed weighting may misrepresent narrower operating ranges, making Froude-range selection and weighting essential.The discussion says GenHull E would be favored for operation predominantly below Fn = 0.2, but disadvantageous from Fn = 0.25 to 0.30.Source: §4.1 · p. 22

4.2. Bulbous Bow Representation in the Parametric Hull Model

  • None of 108 bulb-parameter configurations produced a rounded bulb: the representation yielded a constant-width cylindrical forebody and included an ineffective nominal bulb parameter.Integral form coefficients alone cannot establish local geometry or resistance; verification also requires local geometry or resolved resistance computation.Source: §4.2 · p. 22
  • At Fn = 0.152, GenHull A had 27.7% higher total resistance than KCS, while bulb-disabled GenHull E had 7.8% lower resistance; GenHull A’s excess came from viscous pressure drag.Both comparisons used the same meshing rules.Source: §4.2 · p. 22

4.3. Transverse Stability and the Objective Function

  • GenHull E meets intact-stability criteria up to a vertical center of gravity of 13.49 m, yet its permissible center-of-gravity limit is 1.04 m below KCS, or 1.29 m lower under an operational metacentric-height requirement.The reward includes no stability term; its wetted-surface-based friction term can credit reduced wetted area without registering the accompanying loss of initial stability.Source: §4.3 · pp. 22–23
  • A feasibility screen and an objective term are not equivalent: without a stability gradient, optimization may reduce the stability margin to the admissible limit, while hull rankings depend on the stability measure.GenHull E is less stiff near upright but reaches a larger maximum righting lever at a greater heel angle.Source: §4.3 · p. 23

4.4. Requirements for a CFD-Based Reward

  • Reliable generative optimization requires geometric expressivity and reward fidelity together: the current representation cannot express a faired bulb, and the reward omits viscous-pressure effects.A richer representation with the current reward could rank new geometries incorrectly; a higher-fidelity reward with the current representation cannot recover unavailable geometries.Source: §4.4 · p. 23

5. Conclusion

The study combines localized reward-directed diffusion design with viscous CFD assessment of a generated variant and an expert-refined hull. CFD reveals speed-dependent resistance tradeoffs and limitations in geometry, reward evaluation, and stability treatment.

5. Conclusion

  • Parametric masking and surrogate-guided sequential Monte Carlo generated localized hull variants with lower empirically predicted calm-water resistance than KCS.The assessment covered one sampled variant and a hull refined by a naval architect toward KCS.Source: §5 · p. 24
  • The automated CFD pipeline was validated against two benchmark container ships at six speeds each, with total-resistance errors from +14.0% to −8.9% for KCS and −4.1% to −7.5% for DTC.Skin friction did not converge under grid refinement on either hull, so the authors support comparative assessment at matched Froude number rather than precise absolute prediction.Source: §5 · p. 24
  • GenHull E has 6–8% lower total resistance than KCS up to Fn = 0.240, is equal within the confidence interval at Fn = 0.250, and is higher above that speed; Model 1 is 45–50% higher at Fn = 0.250 and 0.260.At Fn = 0.250, an 8.07 N friction advantage nearly cancels an 8.49 N pressure penalty; aggregating across the crossover obscures opposing trends.Source: §5 · p. 24
  • The tested bulb representation could not produce a rounded bulb, the reward omitted viscous pressure and stability terms, and GenHull E lost 1.04 m of permissible vertical center-of-gravity margin despite meeting intact-stability criteria.The authors conclude that matching integral form coefficients and passing feasibility checks do not establish hydrodynamic performance or preserve stability margins.Source: §5 · pp. 24–25
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