High dimensional model representation for piece‐wise continuous function approximation

High dimensional model representation (HDMR) approximates multivariate functions in such a way that the component functions of the approximation are ordered starting from a constant and gradually approaching to multivariance as we proceed along the terms like first‐order, second‐order and so on. Until now HDMR applications include construction of a computational model directly from laboratory/field data, creating an efficient fully equivalent operational model to replace an existing time‐consuming mathematical model, identification of key model variables, global uncertainty assessments, efficient quantitative risk assessments, etc. In this paper, the potential of HDMR for tackling univariate and multivariate piece‐wise continuous functions is explored. Eight numerical examples are presented to illustrate the performance of HDMR for approximating a univariate or a multivariate piece‐wise continuous function with an equivalent continuous function.