Reduced Order Model Base Creation with Bayesian Optimization

Abstract

This research considers the offline training stage of the Reduced Order Models (ROM), that has been getting attention recently on the endeavor to come up with efficient solutions for the highly complex numerical models. In this work, a simply supported beam problem has been considered, for which a reduced basis creation has been investigated. Reduced basis creation is in utmost importance for the accuracy and reliability of the ROM. Main focus is on the efficient parameter sampling strategies to enrich the reduced basis, which brings forth computational burden. To decrease this burden, a statistical tool Gaussian Processes Regression (GPR) based Bayesian Optimization (BO) is utilized. These tools are used to create a surrogate function of error indicator that is used to select additional training points for ROM. Results of this work show that randomness in the proposed procedure influences parameter sampling but does not have an impact on the overall accuracy. Finally, this work suggests further work on creation of a stopping criteria and finding a method of storing previous information and combining it with current information regarding training points without losing information. With the help of proposed further research topics, this work intends to be used as a foundation for efficient reduced basis construction.