Enhancing CFD predictions in shape design problems by model and parameter space reduction

Abstract

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

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• Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference
• A Dynamic Mode Decomposition Extension for the Forecasting of Parametric Dynamical Systems
• A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems
• A DeepONet multi-fidelity approach for residual learning in reduced order modeling
• On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis
• An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques
• 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
• An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations
• Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering
• Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
• An optimisation-based domain-decomposition reduced order model for parameter-dependent non-stationary fluid dynamics problems
• Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation
• A Continuous Convolutional Trainable Filter for Modelling Unstructured Data
• A local approach to parameter space reduction for regression and classification tasks
• Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces