A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces

Abstract

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions -computed for properly chosen parameters, using a full-order model -in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI) -a data-driven reduced order method -with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one. * nicola.demo@sissa.it †

Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing

“…Let us initially assume that the input/output relationship of the problem under study is represented by function f (µ) : Ω ⊂ R n → R. The reduction is performed by computing a linear transformation of the original parameters µ M = Aµ, in which A is an M × n matrix, and M < n. In the last years AS has been extended to vector-valued output functions [46], and to nonlinear transformations of the input parameters using the kernel-based active subspaces (KAS) method [48]. AS has been also coupled with reduced order methods such as POD-Galerkin [49] in cardiovascular studies, and POD with interpolation [50] and dynamic mode decomposition [51] for CFD applications. Application to multi-fidelity approximations of scalar functions are also presented in [52,53].…”

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

“…Active subspaces have also been proven as a useful tool to enhance model order reduction techniques such as proper orthogonal decomposition (POD) with interpolation for structural and fluid dynamics problems [17], and POD-Galerkin methods for a parametric study of carotid artery stenosis [49].…”

PyGeM: Python Geometrical Morphing

“…In the naval field FFD has gained lots of attention thanks for its application to CAD files, for example in shape optimization studies [12][13][14][15][16][17], or in the context of isogeometric analysis [18]. For nautical application we mention [19], while for a benchmark CFD application see [20], where they also perform a reduction of the FFD parameters. The package has been successfully adopted also in automotive engineering, for example in [21,22].…”