Hull shape design optimization with parameter space and model reductions, and self-learning mesh morphing

Abstract

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

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• A DeepONet multi-fidelity approach for residual learning in reduced order modeling
• ATHENA: Advanced Techniques for High Dimensional Parameter Spaces to Enhance Numerical Analysis
• Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method
• Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering
• Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation
• A Shape Optimization Pipeline for Marine Propellers by means of Reduced Order Modeling Techniques
• A local approach to parameter space reduction for regression and classification tasks
• Elasticity-based morphing technique and application to reduced-order modeling
• Data-driven parameterization refinement for the structural optimization of cruise ship hulls