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

math.APOct 9, 2026

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

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

Organizations: Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada · Elomatic Consulting Inc., Vancouver, BC, Canada · InnovMarine Inc., Lévis, QC, Canada

Abstract

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.

Figures & tables

Figure 1: Schematic of the ship-hull optimization workflow with a partially variable design vector. The framework comprises data generation, training of a denoising diffusion probabilistic model (DDPM) and a deep residual surrogate model, reward-guided sampling via sequential Monte Carlo (SMC), and CFD assessment of a sampled variant and of a hull refined by a naval architect.

Parameter	Value
Input dimension ( $D$ )	44
Hidden dimension ( $H$ )	256
Activation	ReLU
Output dimension	$44$
Optimizer	AdamW
Loss function	Mean squared error (MSE)

Table 1: Parameters and hyperparameters for training DDPM

Parameter	Specification
Hidden dimension	256 neurons
Residual block	Linear(256,256)
Optimizer	AdamW
Learning rate	$5\times 10^{-4}$
Weight decay	$1\times 10^{-4}$
Batch size	256

Table 2: ResNet regression model parameters

w^{[i]}\leftarrow\frac{p_{t-1}^{\mathrm{pre}}\!\left(x_{t-1}^{[i]}\mid x_{t}^{[i]}\right)\,\exp\!\left(\hat{v}_{t-1}\!\left(x_{t-1}^{[i]}\right)/\alpha\right)}{q_{t-1}\!\left(x_{t-1}^{[i]}\mid x_{t}^{[i]}\right)\,\exp\!\left(\hat{v}_{t}\!\left(x_{t}^{[i]}\right)/\alpha\right)}\;w^{[i]}.

Algorithm 1 SMC-Based Guidance

Figure 2: Computational mesh generated for the KCS hull, shown on the centerplane: (a) domain and refinement regions; (b) free-surface refinement bands; (c) hull surface and waterline refinement; (d) prism layers at the bow.

$F_{n}$	$y^{+}$	$C_{T}\times 10^{3}$	95 % CI	EFD $\times 10^{3}$	$\varepsilon_{T}$ [%]	$C_{Fv}$ vs ITTC-57 [%]
0.108	25	4.326	$\pm 0.08\,\%$	3.796	$+14.0$	$+6.3$
0.152	32	3.886	$\pm 0.40\,\%$	3.641	$+6.7$	$+2.9$
0.195	39	3.455	$\pm 0.90\,\%$	3.475	$-0.6$	$-2.1$
0.227	44	3.361	$\pm 0.24\,\%$	3.467	$-3.1$	$-4.5$
0.260	48	3.382	$\pm 0.46\,\%$	3.711	$-8.9$	$-6.3$
0.282	60	4.148	$\pm 0.55\,\%$	4.501	$-7.8$	$-7.8$

Table 3: Validation of the CFD pipeline against KCS model-scale measurements.

\varepsilon_{T}

is the error in total resistance coefficient relative to experiment.

Figure 3: Computed and measured total resistance coefficients for KCS (top) and the corresponding comparison error (bottom). The shaded band indicates the Froude number range targeted for CFD-based training data.

$F_{n}$	$Re$	$C_{T}\times 10^{3}$	95 % CI	EFD $\times 10^{3}$	$\varepsilon_{T}$ [%]	$C_{Fv}$ vs ITTC-57 [%]
0.174	$7.30\times 10^{6}$	3.511	$\pm 1.15\,\%$	3.661	$-4.1$	$-4.4$
0.183	$7.68\times 10^{6}$	3.451	$\pm 0.96\,\%$	3.605	$-4.3$	$-5.2$
0.192	$8.06\times 10^{6}$	3.373	$\pm 0.68\,\%$	3.588	$-6.0$	$-6.5$
0.200	$8.40\times 10^{6}$	3.357	$\pm 0.95\,\%$	3.602	$-6.8$	$-6.1$
0.209	$8.77\times 10^{6}$	3.417	$\pm 0.78\,\%$	3.623	$-5.7$	$-5.7$
0.218	$9.15\times 10^{6}$	3.394	$\pm 0.90\,\%$	3.670	$-7.5$	$-6.2$

Table 4: Validation of the CFD pipeline against DTC model-scale measurements, using the same rule set as for KCS.

Figure 4: Computed and measured total resistance coefficients for DTC (top) and the corresponding comparison and skin-friction errors (bottom).

Figure 5: Denoising and reverse-step accuracy of the trained diffusion model on held-out hull designs. The left axis shows the mean squared error per dimension between the predicted and known forward-diffusion noise. The logarithmic right axis shows the conditional Gaussian posterior KL divergence, in nats per dimension, between the reference reverse-step posterior conditioned on the known clean hull and the trained reverse kernel using featurewise bounded denoised estimates. Both metrics are plotted against forward diffusion time; lower values indicate greater accuracy.

Figure 6: Normalized ESS during SMC sampling. The dashed line marks the resampling threshold of 0.5. The solid curve shows the mean and the shaded band shows an approximate pointwise 95% confidence interval across five sampler seeds, with the trained models held fixed. ESS is evaluated before resampling.

Figure 7: Profile (top) and three-quarter (bottom) views of the KCS, DTC and GenHull E hull forms.

Quantity	KCS	GenHull E	Difference
$L_{pp}$ [m]	230.00	230.00	constrained
$L_{wl}$ [m]	232.19	230.30	$-0.81\,\%$
$B_{wl}$ [m]	32.22	34.46	$+6.96\,\%$
$T$ [m]	10.80	10.80	$-0.01\,\%$
$\nabla$ [m 3 ]	51 765	52 042	$+0.53\,\%$
$S$ [m 2 ]	9 462	8 802	$-6.97\,\%$

Table 5: Principal particulars and form coefficients of KCS and GenHull E at full scale, computed from the as-meshed geometry at design draft.

Figure 8: Cross curves of stability (left) and righting-arm curves at $KG=13.0$ m (right) for KCS and GenHull E at design draft.

$F_{n}$	$R_{T}$ KCS	$R_{T}$ GenHull E	$\Delta R_{T}$	$\Delta$ pressure	$\Delta$ friction	separation
	[N]	[N]	[%]	[N]	[N]
0.152	30.418	28.042	$-7.81$	$+0.78$	$-3.15$	—
0.195	44.596	40.843	$-8.42$	$+2.06$	$-5.81$	—
0.227	59.147	55.377	$-6.37$	$+3.58$	$-7.35$	2.1
0.240	65.366	60.661	$-7.20$	$+3.18$	$-7.88$	1.9
0.250	70.053	70.480	$+0.61$	$+8.49$	$-8.07$	0.2

Table 6: Total resistance of GenHull E and KCS at model scale

1{:}31.6

, with the pressure and friction components of the difference.

Figure 9: Total resistance of GenHull E relative to KCS (left) and the pressure and friction components of the difference (right). The shaded band indicates the Froude number range targeted for CFD-based training data.

Figure 10: Free-surface elevation, normalized by $U^{2}/2g$ , for KCS (top) and GenHull E (bottom) at five Froude numbers.

Figure 11: Pressure coefficient on the wetted forebody of KCS (top) and GenHull E (bottom) at $F_{n}=0.227$ and $0.270$ .

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Open paper AskPDF arXiv

Ship-form design combines smooth geometric representation, local shape editing, and constraints on the resulting hull. We present the Natural-Language-to-Hull Framework (NL2Hull Framework), which formulates ship-form editing as a typed discrete decision problem and connects language decisions to numerical geometry. Its Constrained Free-Form Deformation Engine (CFFD Engine) represents hull waterlines with non-uniform rational B-splines (NURBS), applies free-form deformation (FFD) to their control points, reconstructs the hull, and checks geometric constraints. We construct the Ship Design Decision Dataset (SDD Dataset) with 134,558 cleaned records and evaluate compared models on its subset Ship Design Decision Benchmark (SDDBench), containing 5,000 records and 43,496 typed questions. We propose Chip, a constrained ship-design decision model for processing natural-language requests. Chip reaches 95.90% question accuracy and 99.32% FFD exact match, with a negative log-likelihood of 0.0951, an expected calibration error of 0.0032, and a Brier score of 0.0551. The NL2Hull Framework provides a reproducible interface for evaluating language-based ship-form decisions while identifying the geometry and continuous-control components that require further development. Our code and dataset is available at https://github.com/wenhuahuo/NL2Hull.

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