In many areas of science and technology one faces a problem of replacing computationally expensive multivariate functions by efficiently computable approximants. However, obtaining such approximants is still considerably difficult. High Dimensional Model Representation (HDMR) techniques, elaborated in recent years, overcome some of the difficulties, but there is still a lot to be done to make such techniques automatic. To make a progress is this area, we have been developing an adaptive strategy for generating the so-called multicut-HDMR approximants possessing a preselected accuracy. The strategy combines an error-driven cut point addition with an adaptive interpolation of HDMR expansion terms.

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