A Training Set Subsampling Strategy for the Reduced Basis Method

by   Sridhar Chellappa, et al.

We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits the potential of the pivoted QR decomposition and the discrete empirical interpolation method to identify important parameter samples. It consists of two stages. In the first stage, we construct a low-fidelity approximation to the solution manifold over a fine training set. Then, for the available low-fidelity snapshots of the output variable, we apply the pivoted QR decomposition or the discrete empirical interpolation method to identify a set of sparse sampling locations in the parameter domain. These points reveal the structure of the parametric dependence of the output variable. The second stage proceeds with a subsampled training set containing a by far smaller number of parameters than the initial training set. Different subsampling strategies inspired from recent variants of the empirical interpolation method are also considered. Tests on benchmark examples justify the new approach and show its potential to substantially speed up the offline stage of the Reduced Basis Method, while generating reliable reduced-order models.


An iterative multi-fidelity approach for model order reduction of multi-dimensional input parametric PDE systems

We propose a parametric sampling strategy for the reduction of large-sca...

Multi-level adaptive greedy algorithms for the reduced basis method

The reduced basis method (RBM) empowers repeated and rapid evaluation of...

An Adaptive Sampling Approach for the Reduced Basis Method

The offline time of the reduced basis method can be very long given a la...

Adaptive Interpolatory MOR by Learning the Error Estimator in the Parameter Domain

Interpolatory methods offer a powerful framework for generating reduced-...

Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height

In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model...

Multi-fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Model order reduction usually consists of two stages: the offline stage ...

The non-intrusive reduced basis two-grid method applied to sensitivity analysis

This paper deals with the derivation of Non-Intrusive Reduced Basis (NIR...

Please sign up or login with your details

Forgot password? Click here to reset