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We introduce a deep machine learning approach to studying quasar microlensing light curves for the first time by analysing hundreds of thousands of simulated light curves with respect to the accretion disc size and temperature profile. Our results indicate that it is possible to successfully classify very large numbers of diverse light-curve data and measure the accretion disc structure. The detailed shape of the accretion disc brightness profile is found to play a negligible role. The speed and efficiency of our deep machine learning approach is ideal for quantifying physical properties in a 'big-data' problem set-up. This proposed approach looks promising for analysing decade-long light curves for thousands of microlensed quasars, expected to be provided by the Large Synoptic Survey Telescope. [ABSTRACT FROM AUTHOR]