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An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques

Nicola Demo, Giulio Ortali, Gianluca Gustin, Gianluigi Rozza, Gianpiero Lavini

TL;DR

The paper tackles naval hull shape optimization under computationally expensive PDEs by introducing a modular, data-driven ROM framework that couples FFD-based geometry parametrization with ROM surrogates. It leverages DMD for regime prediction and POD-GPR for fast, probabilistic mapping from design parameters to reduced outputs, enabling rapid GA-driven optimization while validating promising designs with high-fidelity FV-RANS-VOF simulations. Applied to a cruise-ship hull, the approach yields substantial speedups (offline/online split) and delivers a meaningful resistance reduction (approximately $3.3\%$ after validation), demonstrating practical industrial impact. The work emphasizes modularity, data-driven interfaces, and the potential for extension to constrained problems and iterative ROM enhancement, making it attractive for fast design cycles in naval engineering.

Abstract

This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation (FFD). The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive -- especially dealing with complex industrial geometries -- we propose also a dynamic mode decomposition (DMD) enhancement to reduce the computational cost of a single numerical simulation. The real--time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression (POD-GPR) technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques

TL;DR

The paper tackles naval hull shape optimization under computationally expensive PDEs by introducing a modular, data-driven ROM framework that couples FFD-based geometry parametrization with ROM surrogates. It leverages DMD for regime prediction and POD-GPR for fast, probabilistic mapping from design parameters to reduced outputs, enabling rapid GA-driven optimization while validating promising designs with high-fidelity FV-RANS-VOF simulations. Applied to a cruise-ship hull, the approach yields substantial speedups (offline/online split) and delivers a meaningful resistance reduction (approximately after validation), demonstrating practical industrial impact. The work emphasizes modularity, data-driven interfaces, and the potential for extension to constrained problems and iterative ROM enhancement, making it attractive for fast design cycles in naval engineering.

Abstract

This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation (FFD). The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive -- especially dealing with complex industrial geometries -- we propose also a dynamic mode decomposition (DMD) enhancement to reduce the computational cost of a single numerical simulation. The real--time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression (POD-GPR) technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

Paper Structure

This paper contains 14 sections, 22 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction and motivations
  2. The complete computational pipeline
  3. Free-form deformation for shape parametrization
  4. Finite volume for high-fidelity database
  5. Dynamic mode decomposition for regime state prediction
  6. Reduced order model exploiting proper orthogonal decomposition
  7. Genetic algorithm for global optimization
  8. Numerical results: a cruise ship shape optimization
  9. Free-form deformation
  10. Finite volume discretization
  11. Dynamic mode decomposition
  12. Proper orthogonal decomposition with Gaussian process regression
  13. Genetic algorithm
  14. Conclusion and future perspectives

Figures (11)

  • Figure 1: The flowchart of the complete computational pipeline.
  • Figure 2: The undeformed hull.
  • Figure 3: $x$- and $y$-normal view of the set $D$ (in blue) and the lattice of points $P^0_{l,m,n}$ (in red) over the undeformed hull.
  • Figure 4: Example of shape morphing with $\boldsymbol{\mu}~=~[0.08, 0.08, -0.06, 0.08, -0.08, 0.08]$
  • Figure 5: The refined computational grid
  • ...and 6 more figures