Efficient surrogate construction by combining response surface methodology and reduced order modeling

Response surface methodology is an efficient method for approximating the output of complex, computationally expensive codes. Challenges remain however in decreasing their construction cost as well as in approximating high dimensional output instead of scalar values. We propose a novel approach addressing both these challenges simultaneously for cases where the expensive code solves partial differential equations involving the resolution of a large system of equations, such as by finite element. Our method is based on the combination of 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 only at a small, appropriately chosen, number of points. At the other points only the inexpensive reduced basis solution is computed while controlling the quality of the approximation being sought. A first application of the proposed surrogate modeling approach is presented for the problem of identification of orthotropic elastic constants from full field displacement measurements based on a tensile test on a plate with a hole. A surrogate of the entire displacement field was constructed using the proposed method. A second application involves the construction of a surrogate for the temperature field in a rocket engine combustion chamber wall. Compared to traditional response surface methodology a reduction by about an order of magnitude in the total system resolution time was achieved using the proposed sequential surrogate construction strategy.