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The field of polymer membrane design is primarily based on empirical observation, which limits discovery of new materials optimized for separating a given gas pair. Instead of relying on exhaustive experimental investigations, we trained a machine learning (ML) algorithm, using a topological, path-based hash of the polymer repeating unit. We used a limited set of experimental gas permeability data for six different gases in ~700 polymeric constructs that have been measured to date to predict the gas-separation behavior of over 11,000 homopolymers not previously tested for these properties. To test the algorithm’s accuracy, we synthesized two of the most promising polymer membranes predicted by this approach and found that they exceeded the upper bound for CO 2 /CH 4 separation performance. This ML technique, which is trained using a relatively small body of experimental data (and no simulation data), evidently represents an innovative means of exploring the vast phase space available for polymer membrane design.