The total infrared (IR) luminosity (L_IR_) can be used as a robust measure of a galaxy's star formation rate (SFR), even in the presence of an active galactic nucleus (AGN), or when optical emission lines are weak. Unfortunately, existing all sky far-IR surveys, such as the Infrared Astronomical Satellite (IRAS) and AKARI, are relatively shallow and are biased towards the highest SFR galaxies and lowest redshifts. More sensitive surveys with the Herschel Space Observatory are limited to much smaller areas. In order to construct a large sample of L_IR_ measurements for galaxies in the nearby Universe, we employ artificial neural networks (ANNs), using 1136 galaxies in the Herschel Stripe 82 sample as the training set. The networks are validated using two independent data sets (IRAS and AKARI) and demonstrated to predict the L_IR_ with a scatter {sigma}~0.23dex, and with no systematic offset. Importantly, the ANN performs well for both star-forming galaxies and those with an AGN. A public catalogue is presented with our L_IR_ predictions which can be used to determine SFRs for 331926 galaxies in the Sloan Digital Sky Survey (SDSS), including ~129000 SFRs for AGN-dominated galaxies for which SDSS SFRs have large uncertainties.