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The application of artificial neural networks (ANNs) for the estimation of HI gas mass fraction (\fgas) 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 \fgas\ scaling relations with a smaller scatter (0.22 dex) than traditional linear fits (0.32 dex), 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 \fgas. 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 (\sigf), we develop a strategy for quantifying which SDSS galaxies our ANN can be adequately applied to, and the associated errors in the \fgas\ estimation. In contrast to previous works, our \fgas\ estimation has no systematic trend with galactic parameters such as M$_{\star}$, $g-r$ and SFR. We present a catalog of \fgas\ estimates for more than half a million galaxies in the SDSS, of which $\sim$ 150,000 galaxies have a secure selection parameter with average scatter in the \fgas\ estimation of 0.22 dex.