Our training dataset, Dataset A, consists of 778 homopolymers (353 unique polymer chemistries), but not all entries have gas permeability data reported on all six gases under study: He, H2, O2, N2, CO2, and CH4. Dataset A is manually collected from the PoLyInfo database (experimental data from before 2005) and is merged with data from the MSA database (beyond 2005). As shown in Fig. ), in general, the more recent MSA database contains polymers with higher permeability, e.g., CO2 permeability greater than 10 3 Barrers, and entries that surpass the 2008 Robeson upper bound. Fig. ) also show that there is not a significant difference when missing gas permeabilities are imputed via extremely randomized trees (ERT) vs Bayesian linear regression (BLR). In these plots, we identify several known PIMs, with their corresponding chemical structures shown in Fig. ). Many of these PIMs are ladder polymers, which have two connection points between consecutive monomers, such as PIM I and PIM II. Some of the polymers are polyimides, such as PIM III. Further visualizations of the results of the imputation process can be found in Fig. Thus, our motivation for constructing Datasets C and D is for rationally targeted exploration of the polymer design space, based on the established interest in PIMs within the membrane design community. Firstly, polyimides have garnered significant attention due to their superior permeability/selectivity tradeoff and high chemical and physical stability, largely due to a rigid aromatic backbone . Thus, Dataset C is constructed as 8 million hypothetical polyimides formed by the polycondensation of known diamines/diisocyanates with dianhydrides from the PubChem library . These 8 million hypothetical polyimides significantly expand the current chemical space of around 2000 polyimides in PoLyInfo. Ladder polymers adopt an alternative approach to stiffen the polymer backbone. These unique polymers have two-bond connections between repeating units and thus restricted rotation, except at a contortion site, which is often a spiro-center . In our work, Dataset D contains hypothetical ladder polymers generated through the binary combinations of components of existing ladder polymers , supplemented by a RNN model. More details about the construction of these datasets are provided in Fig. of Supporting