Soyez le premier à aimer ceci
One of the primary drawbacks plaguing wider acceptance of surrogate models is their low fidelity (in general), which can be in a large part attributed to the lack of quantitative guidelines regarding the suitability of different models for diverse classes of problems. In this context, model selection techniques are immensely helpful in ensuring the selection and use of an optimal model for a particular design problem. A novel model selection technique was recently developed to perform optimal model search at three levels: (i) optimal model type (e.g., RBF), (ii) optimal kernel type (e.g., multiquadric), and (iii) optimal values of hyper-parameters (e.g., shape parameter) that are conventionally kept constant. The maximum and the median error measures to be minimized in this optimal model selection process are given by the REES error metrics, which have been shown to be significantly more accurate than typical cross-validation-based error metrics. Motivated by the promising results given by REES-based model selection, in this paper we develop a framework called Collaborative Surrogate Model Selection (COSMOS). The primary goal of COSMOS is to allow the selection and usage of globally competitive surrogate models. More specifically, this framework will offer an open online platform where users from within and beyond the Engineering Design (and MDO) community can submit training data to identify best surrogates for their problem, as well as contribute new and advanced surrogate models to the pool of models in this framework. This first-of-its-kind global platform will facilitate sharing of ideas in the area of surrogate modeling, benchmarking of existing surrogates, validation of new surrogates, and identification of the right surrogate for the right problem. In developing this framework, this paper makes three important fundamental advancements to the original REES-based model selection - (i) The optimization approach is modified through binary coding to allow surrogates with differing numbers of candidate kernels and kernels with differ- ing numbers of hyper-parameters. (ii) A robustness criterion, based on the variance of errors, is added to the existing criteria for model selection. (iii) Users are allowed to perform model selection for a specified region of the input space and not only for the entire input domain, subject to empirical constraints that are related to the relative sample strength of the region. The effectiveness of the COSMOS framework is demonstrated using a comprehensive pool of five major surrogate model-types (with up to five constitutive kernel types), which are tested on two standard test problems and an airfoil design problem.