Polymer solubility is critical for a variety of industrial and research applications such as plastics recycling, drug delivery, membrane science, and microlithography. For novel polymers, it is often an arduous process to find the appropriate solvents for polymer dissolution. Heuristic approaches, such as solubility parameters, provide only limited guidance with respect to solvent prediction and design. The present work highlights a novel data-driven paradigm for solvent selection in polymers. For this purpose, we utilize a deep neural network trained on a massive data set of over 4500 polymers and their corresponding solvents/nonsolvents. This deep-learning framework maps high-dimensional fingerprints/features to compact chemically relevant latent space representations of solvents and polymers. When these low-dimensional representations are visualized, we observe the spontaneous clustering of nonpolar, polar-aprotic, and polar-protic behavior. This large-scale data-driven approach possesses an overall classification accuracy of above 93% (on a hold-out set) and significantly outperforms existing methods to determine polymer/solvent compatibility such as the Hildebrand criteria.