A mathematical “kinetic lumping” approach, the direct constrained approximate lumping (DCAL) method, for developing a condensed chemical mechanism of complex tropospheric alkane photochemistry was presented in previous work. In the present work, the high dimensional model representation (HDMR) method is applied to further accelerate the chemical kinetic calculations of the Alkane/DCAL mechanism from our previous work. An efficient HDMR is based on expressing a chemical species concentration at a given reaction time as an expansion of correlated functions consisting of the initial chemical species concentrations. An HDMR expansion calculates efficiently the output species concentrations at any given reaction time, employing very rapid and stable algebraic manipulations. The HDMR estimates are shown to be almost identical to those derived from solving the full tropospheric alkane photochemistry through conventional (for example, Gear‐type) chemistry solvers over wide ranges of initial conditions, while being more than 1,000 times faster. © 2005 American Institute of Chemical Engineers AIChE J, 2005