A Framework for Guaranteed Error-bounded Surrogate Modeling

We present a data-driven surrogate modeling technique to replace computationally expensive high-fidelity models. The proposed technique uses the Hessian information of the original grey-box/black-box model to construct edge-concave underestimators and edge-convex overestimators to provide approximation over the entire domain with guaranteed error-bounds. A surrogate model with prepostulated form is then achieved by performing a parameter estimation that ensures the approximation to be bounded between the vertex polyhedral under- and over-estimators of the original model. We describe a package named GEMS that integrates and automates the required series of tasks, i.e., the location and the number of sample evaluation, estimation of the Hessian bounds, and parameter estimation to obtain the surrogate with guaranteed prediction within the error bounds. As a case study, we demonstrate that the suggested surrogate by GEMS exhibits good performance in predicting the solubility of hydrofluorocarbon (HFC) refrigerants in ionic liquids (IL).