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

TL;DR

This paper introduces a non-intrusive method combining Proper Orthogonal Decomposition with Active Subspaces to improve reduced order modeling accuracy while reducing the number of high-fidelity solutions needed.

Contribution

It proposes a novel coupling of PODI with Active Subspaces to enhance ROM accuracy with fewer input solutions, applicable to structural and fluid dynamics problems.

Findings

Reduced number of solutions needed for accurate ROM

Effective application to structural and fluid dynamics problems

Improved computational efficiency in parametric simulations

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.