The preliminary design of AUGs is intrinsically challenging due to the strong coupling between the external hydrodynamic shape, the hydrostatic balance, the structural integrity, and internal packaging constraints. This complexity is further amplified for bio-inspired configurations, whose rich geometric parametrizations lead to high-dimensional design spaces that are difficult to explore using conventional optimization approaches. This work presents a ML-enabled bi-level multidisciplinary design optimization (MDO) framework for the performance-driven design of a manta-ray-inspired AUG. At the upper level, hydrodynamically efficient external geometries are explored in a reduced design space obtained through physics-driven parametric model embedding, which identifies a low-dimensional latent representation directly correlated with the lift, drag, and pressure distributions. At the lower level, a constrained internal sizing problem determines the minimum feasible empty weight by accounting for structural, hydrostatic, geometric, and payload constraints. To render the resulting bi-level problem computationally tractable, a multi-fidelity surrogate-based optimization strategy is adopted, combining low- and high-fidelity hydrodynamic models with stochastic radial basis function surrogates and adaptive Bayesian sampling. The framework enables efficient exploration of the coupled design space while rigorously managing model uncertainty and computational cost. The optimized configurations exhibit a 14.7% improvement in maximum hydrodynamic efficiency and a 12.8% reduction in empty weight relative to the baseline design, while satisfying all disciplinary constraints. These results demonstrate that the integration of physics-driven dimensionality reduction and multi-fidelity machine learning enables scalable and physically consistent MDO of complex bio-inspired underwater vehicles.

In this paper, we present new developments and improvements made to a Computational Fluid Dynamics (CFD)-based Dynamic Velocity Prediction Program (DVPP) for predicting sailing yacht performance in waves. The DVPP and its use for computing equilibrium states and predicting the optimal speed of a yacht design were detailed in a previous paper. The enhancements introduced here aim to help naval architects evaluate their designs in more realistic offshore racing conditions. First, waves modelling has been improved and a PID-controlled rudder enabling six degrees of freedom (DoF) simulations can now be used for course control. The computation of aerodynamic forces has been refined to include the effects of added mass. Finally, the sock-mesh approach has been expanded to simulate a fully appended yacht, incorporating foil fluid-structure interaction through a pragmatic method.

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as principal component analysis, are widely used but often neglect the physical response of the system and lack invertibility to the design space, i.e., the ability to reconstruct the original design parameters from a reduced representation. This work introduces two physics-aware extensions of the parametric model embedding (PME) framework, aimed at generating reduced representations that incorporate physical information while maintaining analytical backmapping. The first, physics-informed PME (PI-PME), combines geometric and physical variability; the second, physics-driven PME (PD-PME), relies solely on physical responses. The proposed methods enable the construction of interpretable and physically relevant reduced spaces that can be used for design-space exploration, surrogate modeling, and optimization. The approach is demonstrated on multiple engineering configurations, including airfoils, propellers, gliders, and hulls, showing its ability to capture performance-relevant directions and preserve parametric consistency. The methodology is offline and non-intrusive, compatible with low-fidelity simulations, and requires only a modest number of samples to ensure variance convergence.

Accurate simulations of the flow around lifting hydrofoils are challenging, since they need to capture the flow near the foil surface precisely, represent the free surface, and take into account body motion and deformation. Therefore, these simulations are often computationally expensive. This paper studies numerical methods to limit the costs of hydrofoil simulation. Mesh adaptation is used to efficiently capture the free-surface flow, to resolve flow details around the foil surface, and to ensure the accuracy of mesh motion techniques, like overset meshing. For maximum precision of the boundary-layer flow, adaptation is started from dedicated body-aligned meshes. Hydrofoil flexibility is taken into account through a linear eigenmode-based reduced-order model of the structural response. This approach removes the need to couple directly the fluid and structure solvers and reduces the computational overhead for fluid-structure simulation. Equilibrium positions for flexible and rigid motion are determined with a fixed-point iteration based on quasi-Newton and approximate models for the forces respectively, which eliminate the need for costly time-accurate simulation. Test cases demonstrate that these methods work together, providing accurate simulations of realistic hydrofoils with reasonable computational costs. Mesh adaptation allows to target a specific numerical uncertainty through the refinement threshold parameter. Together with the body-aligned 'sock' meshes, adaptive refinement produces the same accuracy as non-adapted meshes for up to 10 times less CPU hours. Both fluid-structure interaction methods lead to computations which have the same convergence speeds as for non-moving bodies. Thus, foil flexibility can be simulated fora computational overhead below 40% and it leads to significantly better agreement with experiments.

As a first step toward a multi-fidelity optimization tool for hydrofoils, the present work assesses the ability of the in-house code PUFFIn to be used as a “low-fidelity” solver within the multi-fidelity framework. The code, based on the Boundary Element Method (BEM) and the potential flow theory, is used to study the performance of a typical windsurf hydrofoil operating near the free surface. The hydrofoil is composed of a front wing and a rear stabilizer in a plane-like configuration. Computations are performed for single body configurations (only one wing) and two-body configurations (front wing and stabilizer). First, three linearized models of the free surface are compared for the single front wing configuration with several values of the Froude number: the symmetry, anti-symmetry and Neumann-Kelvin conditions. The results show that for relatively high Froude number, the anti-symmetry and the Neumann-Kelvin conditions provide very similar forces. Then, the predictions of the BEM solver are compared with “high-fidelity” RANS computations, in terms of pressure drag and lift, pressure distribution on the hydrofoil and free surface elevation. Several Froude numbers and submergence depths are studied. The global lift and drag variations predicted by the BEM with the anti-symmetry and Neumann-Kelvin conditions on the single-body configurations are similar to the RANS predictions. For the two-body configurations, the Neumann-Kelvin condition outperforms the anti-symmetry condition. Based on the BEM/RANS comparison, the potential flow solver reveals to be a relevant tool for multi-fidelity optimization.

Lifting hydrofoils are gaining importance, since they drastically reduce the wetted surface area of a ship, thus decreasing resistance. To attain efficient hydrofoils, the geometries can be obtained from an automated optimisation process. However, hydrofoil simulations are computationally demanding, since fine meshes are needed to accurately capture the pressure field and the boundary layer on the hydrofoil. Simulation-based optimisation can therefore be very expensive. To speed up the fully automated hydrofoil optimisation procedure, we propose a multi-fidelity framework which takes advantage of both an efficient low-fidelity potential flow solver dedicated to hydrofoils and a high-fidelity RANS solver enhanced with adaptive grid refinement and dedicated foil-aligned overset meshes, to attain high accuracy with a limited computational budget. Both solvers are shown to be reliable for automatic simulation, and remarkable correlation between potential-flow and RANS results is obtained. Two different multi-fidelity frameworks are compared for a realistic hydrofoil: only RANS based and potential-RANS based. According to the optimisation results, the drag is able to be reduced by 17% and 8% in these frameworks, within a realistic time frame. Thus, industrial optimisation of hydrofoils appears possible. Finally, critical areas of future improvement regarding the robustness and efficiency of the optimisation procedure are discussed in this study.

A dynamic Velocity Prediction Program (VPP) integrated in a Computational Fluid Dynamics (CFD) code is described. Aerodynamic forces are obtained either through empirical coefficients or interpolated from aerodynamics matrices. These aerodynamic forces are then input to the hydrodynamics CFD solver, which solves both the flow and the motions of the boat, resulting in a closely coupled VPP. For a given True Wind Angle and True Wind Speed a sail power parameter is optimised to obtain the best possible boat speed within heel angle constraints. This approach allows naval architects to swiftly and precisely compare several yacht designs in real sailing configurations using only a few CFD computations. Several advanced features recently added to this program are covered in this paper including convergence criteria, automatic grid refinement, foil fluid-structure interaction, multiple aerodynamics models and rudder control. Results obtained from our CFD VPP on a 40-feet fast-cruising yacht demonstrates promising agreement with other existing VPP polars, affirming the accuracy and reliability of our approach. The CFD VPP presented was also successfully applied to an IMOCA, a 60-feet racing yacht.

Hybrid RANS/LES (HRL) models use LES in complex regions and RANS otherwise. However, HRL models have issues when dealing with the transition between RANS and LES areas. The goal of this paper is to propose a solution to the lack of a mechanism in the DES model for transferring the modelled turbulent kinetic energy (TKE) to the resolved scales. The presented approach uses a volume forcing which amplifies existing velocity fluctuations. It aims at compensating for the modelled TKE dissipated by reinjecting it as resolved kinetic energy, so that the total TKE is unaffected. This solution's effectiveness is evaluated on a turbulent boundary layer over a flat plate, a case where DES is highly sensitive to mesh refinement. Different meshes and time steps are tested to assess the impact of the method on the flow. This approach shows a clear improvement on the turbulent quantities compared to the DES model.

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Simulation-driven shape optimization often uses surrogate models, i.e. approximate models fitted through a dataset of simulation results for a limited number of designs. The shape optimization is then performed over this surrogate model. For efficiency, modern approaches often construct the datasets adaptively, adding simulation points one by one where they are most likely to discover the optimum design [3]. The uncertainty estimation of the surrogate model is essential to guide the choice of new sample points: underestimation of the uncertainty leads to sampling in suboptimal regions, missing the true optimum. Gaussian process regression naturally provides uncertainty estimations [4] and Stochastic Radial Basis Functions (SRBF) surrogate models estimate the uncertainty based on the spread of RBF fits with different kernels [5]. In the context of SRBF, this paper discusses two issues with uncertainty estimation. The first is that most existing techniques rely on knowledge about the global behaviour of the data, such as spatial correlations. However, the number of datapoints can be too small to reconstruct this global information from the data. We argue that in this situation, user-provided estimation of the function behaviour is a better choice (section 3). The second issue is that the dataset may contain noise, i.e. random errors without spatial correlation. Surrogate models can filter out this noise, but it introduces two separate uncertainties: the optimum amount of noise filtering is unknown, and for a small dataset (even with perfect noise filtering) the local mean of the data may not correspond to the true simulation response. In section 4 we introduce estimators for both uncertainties.

Lifting hydrofoils are gaining importance, since they drastically reduce the wetted surface area of a ship hull, thus decreasing resistance.To attain efficient hydrofoils, the geometries can be obtained from an automated optimization process, based on simulations.However, hydrofoil high-fidelity simulations are computationally demanding, since fine meshes are needed to accurately capture the pressure field and the boundary layer on the hydrofoil.Moreover, the immersed depth varies dynamically, which makes the simulation of hydrodynamic forces challenging.Simulation-based optimization can therefore be very expensive.Automated surrogate models, trained by a limited number of simulations, can reduce the required computational demand for the optimization process.Furthermore, if an efficient low-fidelity hydrofoil performance prediction tool is available, using surrogate models in a multi-fidelity framework [2] can provide a further reduction in the total required simulation cost, by combining the accuracy of a few high-fidelity simulations with the adequate exploration capability of a greater number of low-fidelity computations.In this study, we propose a hydrofoil optimization procedure based on two simulation methods, a dedicated hydrofoil potential flow solver [1] for low-fidelity and RANS for both medium-and highfidelity.The RANS solver uses adaptive grid refinement [2] to attain maximum accuracy with the lowest computational budget.Moreover, two distinctive improvements are provided within the surrogate modeling process.The first one aims to increase the accuracy of the uncertainty estimation when very few sample points are available and the second one provides better noise-canceling for the data in the sample points, with an estimation of the uncertainty due to the noise filtering.In this study, the proposed automated multi-fidelity surrogate model procedure will be tested for a parameterized geometric model of a realistic hydrofoil.The influence of the surrogate modeling technique and the effect of different combinations of fidelity levels on the efficiency of the optimization and the performance of the hydrofoil will be investigated.

The efficiency of simulation-driven design optimization based on surrogate models, depends strongly on the suitability of the surrogate model for the simulation data on which it is based. We investigate adaptive surrogate modelling methods that maximize the efficiency and the robustness for any optimization problem. Specific techniques include: adaptive sampling, noise filtering by metamodel tuning, and small initial datasets to give maximum freedom to the adaptation. These methodological advancements are demonstrated for an analytical test problem, as well as the shape optimization of the DTMB 5415 ship model for calm-water resistance.

This article describes key issues which have to be addressed to apply Computational Fluid Dynamics to Naval Hydrodynamics.The specific aspects of Naval Hydrodynamics are discussed and illustrated by recent simulations and comparisons with available experiments.Free-surface flows with or without waves and even violent phenomena such as ventilation or cavitation can be modelled with mixture-fluid surface capturing.Turbulence modelling of thick boundary layers and vortical flows requires anisotropic RANS models or hybrid RANS/LES in case of strongly separated flows.Moreover, fluid-structure interaction in the form of rigid or flexible body motion and multi-body systems is crucial to represent ship manoeuvring and propulsion.Finally, the paper underlines the central role played by anisotropic adaptive grid refinement in the accurate simulation of marine flows.

. Adaptive grid refinement is tested for routine, automated simulations of ship resistance in calm water. A simulation protocol for these computations is fine-tuned on one test case and then applied unchanged to three different cases. The solutions are numerically accurate and compare well with experiments. Effective numerical uncertainty estimation increases the trustworthiness of the solutions.