The application of artificial neural networks (ANNs) for the estimation of HI gas mass fraction (M_HI_/M*) is investigated, based on a sample of 13 674 galaxies in the Sloan Digital Sky Survey (SDSS) with HI detections or upper limits from the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA). We show that, for an example set of fixed input parameters (g-r colour and i-band surface brightness), a multidimensional quadratic model yields M_HI_/M* scaling relations with a smaller scatter (0.22dex) than traditional linear fits (0.32dex), demonstrating that non-linear methods can lead to an improved performance over traditional approaches. A more extensive ANN analysis is performed using 15 galaxy parameters that capture variation in stellar mass, internal structure, environment and star formation. Of the 15 parameters investigated, we find that g-r colour, followed by stellar mass surface density, bulge fraction and specific star formation rate have the best connection with M_HI_/M*. By combining two control parameters, that indicate how well a given galaxy in SDSS is represented by the ALFALFA training set (PR) and the scatter in the training procedure ({sigma}_fit_), we develop a strategy for quantifying which SDSS galaxies our ANN can be adequately applied to, and the associated errors in the M_HI_/M* estimation. In contrast to previous works, our M_HI_/M* estimation has no systematic trend with galactic parameters such as M*, g-r and star formation rate. We present a catalogue of M_HI_/M* estimates for more than half a million galaxies in the SDSS, of which ~150000 galaxies have a secure selection parameter with average scatter in the M_HI_/M* estimation of 0.22dex.