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Deep learning has emerged as a promising paradigm to give access to highly accurate predictions of molecular and material properties. A common short-coming shared by current approaches, however, is that neural networks only give point estimates of their predictions and do not come with predictive uncertainties associated with these estimates. Existing uncertainty quantification efforts have primarily leveraged the standard deviation of predictions across an ensemble of independently trained neural networks. This incurs a large computational overhead in both training and prediction, resulting in order-of-magnitude more expensive predictions. Here, we propose a method to estimate the predictive uncertainty based on a single neural network without the need for an ensemble. This allows us to obtain uncertainty estimates with virtually no additional computational overhead over standard training and inference. We demonstrate that the quality of the uncertainty estimates matches those obtained from deep ensembles. We further examine the uncertainty estimates of our methods and deep ensembles across the configuration space of our test system and compare the uncertainties to the potential energy surface. Finally, we study the efficacy of the method in an active learning setting and find the results to match an ensemble-based strategy at order-of-magnitude reduced computational cost.

 

Facile and large-scale synthesis of well-defined, thermally stable silver nanoparticles protected by polymer brushes for use in practical applications is still a challenge. Recent work has reported a nanoreactor approach that can be used to synthesize these silver nanoparticles. This approach uses amphiphilic star-block copolymers, which have a hydrophilic core surrounded by a hydrophobic exterior. These polymers thus can serve as the nanoreactors. In this study, we hypothesize that the local high concentration of silver ions in the inner hydrophilic cores of these star-block copolymers facilitates the nucleation and subsequent growth of silver nanoparticles. When all silver nanoparticles nucleate from the cores of the star-block copolymers in solution, the particle size can be controlled by the core size of the polymer. To test this hypothesis, a polyisoprene-b-poly(p-tert-butylstyrene) (PI-b-PtBS) star-block copolymer was functionalized with carboxylic acid groups using a high-efficiency, photo-initiated thiol-ene click reaction. We characterized this modified polymer using proton nuclear magnetic resonance spectroscopy, and the results indicated that ~60% of the double bonds in the polyisoprene block were successfully functionalized with carboxylic acid groups. When silver ions were added to a solution of these functionalized star-block copolymers, the negatively charged carboxylic acid groups would attract the positively charged silver ions. Subsequent reduction of these Ag+ by a tert-butylamine-borane complex at room temperature produced nanosized silver particles. However, transmission electron microscopy images showed that a significant amount of relatively large silver nanoparticles grew outside the star-block copolymer nanoreactors.