HDMR is a set of quantitative model assessment and analysis tools for capturing high dimensional input-output system behavior. The treatment of high dimensional systems often requires large computational or laboratory sampling efforts, which is known as "curse of dimension". HDMR represents a high dimensional system as a combination of a set of low (e.g., 1 or 2) dimensional systems and dramatically reduces the computational and sampling efforts. Systematic approaches have been developed to construct distinct, but formally equivalent HDMR expansions.

HDMR can be applied for a variety of purposes including construction of a computational model directly from lab/field data, creation of an efficient fully equivalent operational model (FEOM) from an existing time-consuming mathematical model, identification of key model variables, global uncertainly assessments, and inversion of laboratory measurements.