Zone-wise surrogate modelling (ZSM) of univariate systems

Abstract

Many complex systems display distinctly different behaviors across regions, zones, or sub-domains. A single surrogate may not suffice in modelling such systems. A better approach would be to identify the various zones and model them individually. In this work, we propose a zone-wise surrogate modelling (ZSM) algorithm to identify various zones in a system's input domain based on a user-specified acceptable goodness of fit and recommend the best surrogate for each identified zone from a library of potential surrogates. We have assessed ZSM on ten case studies involving complex 1-D functions and compared its modelling performance against some non-linear and piecewise models. We also show how ZSM can help in global optimization using five complex multimodal functions and found that a ZSM-based approach successfully identifies the true global optima of these functions. In future, we aim to extend ZSM for the modelling and optimization of complex multi-input single-output (MISO) systems.