Comptes Rendus
A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces
Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 873-881.

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.

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DOI: 10.1016/j.crme.2019.11.012
Keywords: Reduced order modeling, Proper orthogonal decomposition with interpolation, Reduction in parameter space, Active subspaces, Free form deformation

Nicola Demo 1; Marco Tezzele 1; Gianluigi Rozza 1

1 Mathematics Area, mathLab, SISSA, International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
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Nicola Demo; Marco Tezzele; Gianluigi Rozza. A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces. Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 873-881. doi : 10.1016/j.crme.2019.11.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.11.012/

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