HullFT: Dual Roles in ML & Naval Design

• HullFT is a term denoting dual workflows—convex hull‐based fine-tuning for large language models and modular hull form optimization for ships.
• In the ML context, HullFT employs sparse convex reconstruction, integerization, and gradient caching to accelerate per-query model adaptation.
• In naval design, HullFT integrates free-form deformation, reduced-order modeling, and optimization to enhance hydrodynamics, structural performance, and dynamic response.

HullFT is a term that appears in two distinct research senses. In machine learning, it denotes “convex hull–based fine-tuning”, a test-time finetuning pipeline for LLMs that selects support examples by sparse convex reconstruction of a query embedding and accelerates adaptation through geometric integerization and gradient caching (Khamis et al., 28 May 2026). In naval architecture and offshore engineering, the same label is used conceptually for a Hull Form Tool: a modular workflow for hull parametrization, reduced-order modeling, and optimization, typically combining free-form deformation, active subspaces, dynamic mode decomposition, proper orthogonal decomposition with interpolation, and solver-wrapping for hydrodynamic or structural analysis (Demo et al., 2018, Demo et al., 2018, Tezzele et al., 2022, Lemmer et al., 2020).

1. Terminological scope

The literature uses the term in two domain-specific ways rather than as a single unified method.

Usage of “HullFT”	Domain	Core elements
“convex hull–based fine-tuning”	LLM test-time finetuning	Frank–Wolfe selection, geometric integerization, Gradient Reuse
“Hull Form Tool”	Ship and offshore design	FFD, CFD or FE solvers, DMD, POD/PODI, active subspaces, optimization

In the LLM setting, HullFT is an explicitly named method introduced for per-query adaptation of GPT-style models (Khamis et al., 28 May 2026). In the ship and offshore literature, “HullFT” functions as a convenient description of a modular design environment that couples geometry parametrization, reduced-order modeling, and optimization for hull resistance, structural mass, or dynamic response (Demo et al., 2018, Demo et al., 2018, Tezzele et al., 2022, Lemmer et al., 2020).

A plausible implication is that the commonality between the two usages is methodological rather than disciplinary: both organize an expensive, high-dimensional search around a reduced representation that is cheap to evaluate and operationally interpretable.

2. HullFT in test-time finetuning of LLMs

In "Efficient Test-Time Finetuning of LLMs via Convex Reconstruction and Gradient Caching" (Khamis et al., 28 May 2026), HullFT is a per-query TTFT pipeline. For each query or prompt $q$, the method retrieves a candidate pool of training sequences, selects a small support set, briefly finetunes the model on that support, and then evaluates the adapted model on the query. The stated bottlenecks are data selection and finetuning, both incurred per query.

The selection stage is posed as a convex reconstruction problem. Let the query embedding be $q \in \mathbb{R}^d$, let the candidate pool be $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$, and let $P \in \mathbb{R}^{d \times K}$ have columns $p_i$. HullFT solves

$\min_{w \in \Delta^K} \|q - Pw\|_2^2,$

where $$\Delta^K = \{w \in \mathbb{R}^K: w_i \ge 0,\ \sum_i w_i = 1\}$$. The support set is

$S = \{p_i \mid w_i > 0\}.$

The paper’s interpretation is geometric: a sparse convex combination that approximates $q$ is simultaneously relevant and diverse, because near-duplicate candidates reduce the residual only marginally once one direction has already been represented.

The optimization is carried out with the Frank–Wolfe algorithm over the simplex. Initialization chooses the closest vertex by dot product,

$$v^* = \arg\max_{i \in [K]} \langle q, p_i\rangle,\qquad w^{(0)} = e_{v^*},$$

and each iteration computes the residual $q \in \mathbb{R}^d$0, selects

$q \in \mathbb{R}^d$1

performs a line search for $q \in \mathbb{R}^d$2, and updates

$q \in \mathbb{R}^d$3

The method is explicitly projection-free, and every iterate remains sparse, with support size at most $q \in \mathbb{R}^d$4 after $q \in \mathbb{R}^d$5 iterations. The paper relates this construction to approximate Carathéodory results and uses a support cap $q \in \mathbb{R}^d$6 in practice (Khamis et al., 28 May 2026).

This formulation places HullFT between two established TTFT baselines. Relative to kNN TTFT, it adds a second-stage geometric selector to avoid redundancy among top neighbors. Relative to SIFT, it seeks relevance and diversity without an explicit redundancy penalty or information-gain objective. The paper therefore presents HullFT as a geometric alternative to diversity-aware active selection (Khamis et al., 28 May 2026).

3. Integerization, gradient caching, and empirical performance

The Frank–Wolfe solution is fractional, whereas TTFT requires an explicit multiset of exactly $q \in \mathbb{R}^d$7 examples for finetuning. HullFT therefore solves a discrete approximation problem on the selected support. If the support points are $q \in \mathbb{R}^d$8 with corresponding weights $q \in \mathbb{R}^d$9, the integerization objective is

$\{p_1,\dots,p_K\} \subset \mathbb{R}^d$0

The procedure has three stages: floor allocation $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$1, greedy fill of the remaining copies, and local-swap refinement for a small number of passes. The resulting counts $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$2 define an exact multiset of size $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$3 whose uniform mean approximates the query embedding while preserving the geometry of the Frank–Wolfe solution (Khamis et al., 28 May 2026).

These multiplicities are then exploited through Gradient Reuse. For a block of $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$4 repetitions of a selected sequence $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$5, HullFT recomputes a fresh gradient only every $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$6 steps: $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$7 Because repeated copies are arranged contiguously, the method can reduce forward–backward passes from $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$8 to approximately $\{p_1,\dots,p_K\} \subset \mathbb{R}^d$9 while keeping all $P \in \mathbb{R}^{d \times K}$0 optimizer steps (Khamis et al., 28 May 2026).

The experiments use GPT-2 on 12 subsets of The Pile, with 150 test queries per subset, RoBERTa retrieval embeddings, and a candidate pool of top $P \in \mathbb{R}^{d \times K}$1 nearest neighbors from a FAISS index. Across all total runtime budgets $P \in \mathbb{R}^{d \times K}$2 seconds, HullFT achieves strictly lower BPB% than both kNN and SIFT. Reported margins include a 6.4% lower BPB% than the best baseline at $P \in \mathbb{R}^{d \times K}$3 seconds, 3.83% lower at $P \in \mathbb{R}^{d \times K}$4 seconds, and 3.44% lower at $P \in \mathbb{R}^{d \times K}$5 seconds. Selection is on average 12× faster than SIFT, and on CPU the paper reports 25.8× faster selection, with 0.036 s for HullFT Frank–Wolfe selection versus 0.934 s for SIFT. At $P \in \mathbb{R}^{d \times K}$6, Gradient Reuse yields an average 1.48× speedup in finetuning time, from approximately 5.57 s to 3.76 s, with an average BPB% degradation of about 0.64% (Khamis et al., 28 May 2026).

The paper also reports that HullFT’s BPB% is essentially flat up to $P \in \mathbb{R}^{d \times K}$7 in the Frank–Wolfe tolerance sweep, indicating that the support cap rather than the tolerance is the active control on sparsity. CPU-only experiments on six Pile subsets show that end-to-end runtime savings remain substantial even when selection and finetuning are both resource-constrained (Khamis et al., 28 May 2026).

4. HullFT as a hull-form optimization environment in hydrodynamics

In ship hydrodynamics, the term refers not to a single algorithm but to an integrated optimization environment. "An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment" (Demo et al., 2018) formulates a preliminary-design problem for the DTMB-5415 naval combatant hull in calm-water, constant-speed, unsteady, free-surface flow, using an inviscid, irrotational, fully nonlinear potential-flow model with sinkage and trim. The hull geometry is morphed by free-form deformation,

$P \in \mathbb{R}^{d \times K}$8

with the deformed lattice written as

$P \in \mathbb{R}^{d \times K}$9

and the design vector restricted to

$p_i$0

The quantity of interest is the steady total resistance, combining wave resistance and an ITTC-57 friction estimate. The paper generates 130 FFD-deformed geometries, splits them into 75% training and 25% testing, and applies active subspaces to total resistance and hydrodynamic trim. For a 2D active subspace, total resistance has average relative error about 20% and absolute RMSE about 1.8 N, whereas hydrodynamic trim has average error about 11% and absolute RMSE about $p_i$1 rad. The same work uses DMD to extrapolate simulations from snapshots between $p_i$2 s and $p_i$3 s up to $p_i$4 s, reducing a full 30 s run from about 24 h to about 10 h, corresponding to roughly a factor 2–2.5 speedup (Demo et al., 2018).

"Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition" (Demo et al., 2018) provides a related but higher-fidelity hull-form workflow for the bulbous bow of a Fincantieri cruise ship at $p_i$5. The geometry is parameterized by five FFD parameters, the high-fidelity solver is an incompressible RANS finite-volume model with SST $p_i$6, and DMD is used to reconstruct the asymptotic state from 20 snapshots between the 50th and 60th second. A total of 62 deformed shapes are sampled, comprising 32 box vertices and 30 uniformly sampled interior points. Proper orthogonal decomposition with interpolation is then built using RBF interpolation with a multiquadric kernel. The optimized hull, when revalidated with the full-order CFD solver, achieves a 2% lower resistance than the original hull, while the error between the high-fidelity resistance and the PODI prediction at the optimal point is about 8% (Demo et al., 2018).

Taken together, these two hydrodynamic studies define the canonical HullFT architecture for early-stage hull-form exploration: FFD for geometry generation, automated meshing and CFD, DMD as a time-acceleration layer, and either active-subspace surrogates or PODI surrogates for low-dimensional exploration and optimization (Demo et al., 2018, Demo et al., 2018).

5. Structural and offshore extensions of the HullFT concept

The structural analogue is developed in "A multi-fidelity approach coupling parameter space reduction and non-intrusive POD with application to structural optimization of passenger ship hulls" (Tezzele et al., 2022). Here the design variables are plate thicknesses over macro areas of a passenger-ship hull, with 20 parameters in a midship case and 16 parameters in a full-hull case. The objective includes plate mass, the mass of additional buckling stiffeners, and quadratic penalties for exceeding limits on yielded and buckled elements: $p_i$7 The underlying FE model is linear elastic and isotropic, solved non-intrusively through MSC Nastran. Input reduction is performed with active subspaces on POD coefficients, output reduction with POD, and multi-fidelity regression with NARGPAS. The reported truncation ranks are $p_i$8 for the midship case and $p_i$9 for the full hull, both with cumulative energy greater than 99.99%. Each optimization begins from 300 full-order evaluations; ROM-based reconstructions of stress fields then take about 1 second per parameter vector. Bayesian optimization is carried out with Emukit, using 400 evaluations per run in the midship case and 600 in the full-hull case. The best NARGPAS design is only 0.23% heavier than the best GPR design in the midship case, and the best NARGPAS design is only 0.08% higher in mass than GPR’s best design in the full-hull case (Tezzele et al., 2022).

A different extension appears in "Semi-Submersible Wind Turbine Hull Shape Design for a Favorable System Response Behavior" (Lemmer et al., 2020), where hull-form tuning is directed not at calm-water resistance or structural mass but at dynamic response. The platform is a three-column semi-submersible with heave plates and a steel tripod, carrying the DTU 10 MW Reference Wind Turbine. The free geometric variables are column spacing $\min_{w \in \Delta^K} \|q - Pw\|_2^2,$0 and heave plate height $\min_{w \in \Delta^K} \|q - Pw\|_2^2,$1, with

$\min_{w \in \Delta^K} \|q - Pw\|_2^2,$2

and the pitch restoring stiffness is fixed at

$\min_{w \in \Delta^K} \|q - Pw\|_2^2,$3

for all hulls by adjusting draft and ballast. The optimum is found near $\min_{w \in \Delta^K} \|q - Pw\|_2^2,$4, $\min_{w \in \Delta^K} \|q - Pw\|_2^2,$5, and $\min_{w \in \Delta^K} \|q - Pw\|_2^2,$6. The paper’s central result is that the optimized semi-submersible responds to first-order wave loads such that the platform rotates in pitch about a point close to the rotor hub, so rotor fore-aft motion is almost unaffected by wave excitation. Tower-base fore-aft fatigue varies by more than 30% across hull designs, and the best design yields tower-base DEL only about 50% higher than the onshore turbine despite severe wave conditions. The work also introduces a frequency-domain indicator based on the minimum 2-norm control effort required to cancel disturbance transmission,

$\min_{w \in \Delta^K} \|q - Pw\|_2^2,$7

as a scalar design criterion for “favorable system response behavior” (Lemmer et al., 2020).

These extensions show that HullFT, in the naval and offshore sense, is not restricted to resistance minimization. It also covers structural sizing, fatigue-sensitive design, hydro-structural coupling proxies, and controller-aware platform shaping (Tezzele et al., 2022, Lemmer et al., 2020).

6. Limitations, assumptions, and research directions

The LLM version of HullFT inherits several constraints from the TTFT setting. It depends on the quality of the upstream retrieval pool and on the geometry induced by a separate RoBERTa encoder rather than the base GPT-2 loss landscape. Integerization is heuristic, not theorem-backed, and the method is less differentiated in very small-budget regimes such as $\min_{w \in \Delta^K} \|q - Pw\|_2^2,$8–3. The paper also notes that scaling beyond the reported $\min_{w \in \Delta^K} \|q - Pw\|_2^2,$9 may require additional engineering, especially in the integerization stage (Khamis et al., 28 May 2026).

The hull-design lineage has a different set of limitations. The DTMB-5415 study uses inviscid potential flow, viscous resistance estimated a posteriori via ITTC-57, only 8 bow-localized FFD parameters, and a single operating condition at $$\Delta^K = \{w \in \mathbb{R}^K: w_i \ge 0,\ \sum_i w_i = 1\}$$0; it also does not detail gradient computation for active subspaces (Demo et al., 2018). The Fincantieri PODI study reports a ROM error at the optimum of about 8%, larger than the achieved 2% resistance improvement, and its ROM is built for a single Froude number (Demo et al., 2018). The passenger-ship structural study assumes linear elastic isotropic material, static hogging and sagging load cases, no fluid–structure interaction, and continuous treatment of thickness variables that are discrete in practice (Tezzele et al., 2022). The semi-submersible study uses first-order potential-flow hydrodynamics with radiation damping neglected in the low-order model, simplified aerodynamics, a single tower mode, and a fixed SISO PI control structure (Lemmer et al., 2020).

The research directions stated across these works are correspondingly diverse. In TTFT, likely extensions include model-aware embeddings, hybridization with RAG, other modalities, and theoretical work on integerization (Khamis et al., 28 May 2026). In the naval and offshore literature, the recurring proposals are more integrated automation of geometry-to-solver pipelines, adaptive sampling, multi-objective and multi-fidelity optimization, coupling with viscous RANS solvers for validation, more extensive FFD parametrizations, and broader hydro-structural-controller co-design (Demo et al., 2018, Demo et al., 2018, Tezzele et al., 2022, Lemmer et al., 2020).

Taken together, these works suggest that “HullFT” is best understood as a family of reduction-driven workflows rather than a single disciplinary artifact. In one branch, the “hull” is a convex hull in embedding space; in the other, it is a ship or offshore hull in physical space. In both branches, the governing principle is to replace expensive high-dimensional search with a sparse or low-dimensional representation that preserves the variables most relevant to the target response.