Cyclical inverse interpolation: An approach for the inverse interpolation of black‐box models using tensor product representations

Abstract

AbstractThis paper proposes a novel approach to inverse interpolating black‐box models, referred to as the cyclical inverse interpolation method (CIIM). The approach relies on the use of a multivariate surrogate function, expressed as a tensor product (TP) model, to systematically generate candidate inputs to the given black‐box model with the goal of obtaining interpolated outputs. While the proposed approach is largely agnostic as to the form of this surrogate function, some of its properties, such as the semantics of its input dimensions with respect to the black box model, are constructively defined. The paper demonstrates the viability of the proposed approach both from a theoretical perspective and through numerical examples. Based on these results, it is argued that the approach can be used for the exploratory identification of black‐box models that have scalar‐valued outputs and can be particularly useful in working with black‐box models that have a large number of inputs and exhibit highly nonlinear behavior.