The key points approach: combining response surface methodology and reduced order modeling to achieve drastic reduction in surrogates construction cost
Résumé
An efficient, thus popular approach for approximating the response of a computationally expensive model is through response surface methodology. Nevertheless, decreasing the surrogate construction cost and improving the handling of high dimensional output remain active topics of research. This paper describes a new approach for addressing both these challenges simultaneously for those types of codes involving the resolution of large systems of equations, such as typically finite element codes. The proposed method is based on the interaction between response surface methodology and reduced order modeling by projection, also known as reduced basis modeling. The novel idea is to carry out the full resolution of the system of equations only at a small, appropriately chosen, number of points. At all the remaining points, only an inexpensive reduced basis solution is calculated. A specific error criterion allows to control the quality of the approximation by determining whether additional full system resolutions are necessary or whether the reduced basis solutions are sufficient. An application example is provided involving the construction of a surrogate for the temperature field in a rocket engine combustion chamber wall. The proposed sequential surrogate construction strategy allowed a reduction by about an order of magnitude in the total system resolution time compared to the traditional response surface construction.