Parametric model order reduction with an adaptive greedy sampling approach based on surrogate modeling. An application of the pMOR in financial risk analysis
Speaker: Onkar Jadhav (Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg)
Title: Parametric model order reduction with an adaptive greedy sampling approach based on surrogate modeling. An application of the pMOR in financial risk analysis
Time: Wednesday, 2022.03.02, 10:00 a.m. (CET)
Place: fully virtual (contact Dr. Jakub Lengiewicz to register)
Format: 30 min. presentation + 30 min. discussion
Abstract: The numerical simulation of physical systems typically involves the solution of large-scale systems of equations resulting from the discretization of PDEs. Model order reduction techniques are very advantageous to overcome this computational hurdle. Based on the proper orthogonal decomposition approach, the talk will present a model order reduction approach for parametric high dimensional convection-diffusion-reaction partial differential equations. The proper orthogonal decomposition requires solving the high dimensional model for some training parameters to obtain the reduced basis. In this work, the training parameters are chosen based on greedy sampling approaches. We propose an adaptive greedy sampling approach that utilizes an optimized search based on surrogate modeling for the selection of the training parameter set. The work also presents an elegant approach for monitoring the convergence of the developed greedy sampling approach along with its error and sensitivity analysis.
The developed techniques are analyzed, implemented, and tested on industrial data of a floater with caps and floors under the one-factor Hull-White model. The results illustrate that the model order reduction approach provides a significant speedup with excellent accuracy for short-rate models.