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Solar energetic particles (SEPs) are an essential source of space radiation, which are hazards for humans in space, spacecraft, and technology in general. In this paper we propose a deep learning method, specifically a bidirectional long short-term memory (biLSTM) network, to predict if an active region (AR) would produce an SEP event given that (i) the AR will produce an M- or X-class flare and a coronal mass ejection (CME) associated with the flare, or (ii) the AR will produce an M- or X-class flare regardless of whether or not the flare is associated with a CME. The data samples used in this study are collected from the Geostationary Operational Environmental Satellite's X-ray flare catalogs provided by the National Centers for Environmental Information. We select M- and X-class flares with identified ARs in the catalogs for the period between 2010 and 2021, and find the associations of flares, CMEs and SEPs in the Space Weather Database of Notifications, Knowledge, Information during the same period. Each data sample contains physical parameters collected from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Experimental results based on different performance metrics demonstrate that the proposed biLSTM network is better than related machine learning algorithms for the two SEP prediction tasks studied here. We also discuss extensions of our approach for probabilistic forecasting and calibration with empirical evaluation.