A two-stage surrogate modelling approach for the approximation of models with non-smooth outputs

Authors

M. Moustapha, B. Sudret

Abstract

Surrogate modelling has become an important topic in the field of uncertainty quantification as it allows for the solution of otherwise computationally intractable problems. The basic idea in surrogate modelling consists in replacing an expensive-to-evaluate black-box function by a cheap proxy. Various surrogate modelling techniques have been developed in the past decade. They always assume accommodating properties of the underlying model such as regularity and smoothness. However such assumptions may not hold for some models in civil or mechanical engineering applications, e.g., due to the presence of snap-through instability patterns or bifurcations in the physical behavior of the system under interest. In such cases, building a single surrogate that accounts for all possible model scenarios leads to poor prediction capability. To overcome such a hurdle, this paper investigates an approach where the surrogate model is built in two stages. In the first stage, the different behaviors of the system are identified using either expert knowledge or unsupervised learning, i.e. clustering. Then a classifier of such behaviors is built, using support vector machines. In the second stage, a regression-based surrogate model is built for each of the identified classes of behaviors. For any new point, the prediction is therefore made in two stages: first predicting the class and then estimating the response using an appropriate recombination of the surrogate models. The approach is validated on two examples, showing its effectiveness with respect to using a single surrogate model in the entire space.