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More than 90% of the world’s hydrogen (H₂) is produced from fossil fuel sources, which requires energy-intensive separation and purification to produce high-purity H₂fuel and to capture the carbon dioxide (CO₂) by-product. While membranes can decarbonize H₂/CO₂separation, their moderate H₂/CO₂selectivity requires secondary H₂purification by pressure swing adsorption. Here, we report hyperselective carbon molecular sieve hollow fiber membranes showing H₂/CO₂selectivity exceeding 7000 under mixture permeation at 150°C, which is almost 30 times higher than the most selective nonmetallic membrane reported in the literature. The membrane is able to maintain an ultrahigh H₂/CO₂selectivity over 1400 under mixture permeation at 400°C. Pore structure characterization suggests that highly refined ultramicropores are responsible for effectively discriminating the closely sized H₂and CO₂molecules in the hyperselective carbon molecular sieve membrane. Modeling shows that the unprecedented H₂/CO₂selectivity will potentially allow one-step enrichment of fuel-grade H₂from shifted syngas for decarbonized H₂production. 

Training a neural network requires choosing a suitable learning rate, which involves a trade-off between speed and effectiveness of convergence. While there has been considerable theoretical and empirical analysis of how large the learning rate can be, most prior work focuses only on late-stage training. In this work, we introduce the maximal initial learning rate - the largest learning rate at which a randomly initialized neural network can successfully begin training and achieve (at least) a given threshold accuracy. Using a simple approach to estimate the maximal initial learning rate, we observe that in constant-width fully-connected ReLU networks, the maximal initial learning rate behaves differently from the maximum learning rate later in training. Specifically, we find that the maximal initial learning rate is well predicted as a power of depth times width, provided that (i) the width of the network is sufficiently large compared to the depth, and (ii) the input layer is trained at a relatively small learning rate. We further analyze the relationship between the maximal initial learning rate and the sharpness of the network at initialization, indicating they are closely though not inversely related. We formally prove bounds for the maximal initial learning rate in terms of depth times width that align with our empirical results. 

Abstract Polymers are unarguably the most broadly used membrane materials for molecular separations and beyond. Motivated by the commercial success of membrane‐based desalination and permanent gas separations, glassy polymer membranes are increasingly being studied for hydrocarbon separations. They represent a class of challenging yet economically impactful bulk separations extensively practiced in the refining and petrochemical industry. This review discusses recent developments in membrane‐based hydrocarbon separations using glassy polymer membranes relying on the sorption‐diffusion mechanism. Hydrocarbon separations by both diffusion‐selective and sorption‐selective glassy polymer membranes are considered. Opinions on the likelihoods of large‐scale implementation are provided for selected hydrocarbon pairs. Finally, a discussion of the challenges and outlook of glassy polymer membrane‐based hydrocarbon separations is presented.