Recent advances in computing power have enabled the generation of large datasets for materials, enabling data-driven approaches to problem-solving in materials science, including materials discovery. Machine learning is a primary tool for manipulating such large datasets, predicting unknown material properties and uncovering relationships between structure and property. Among state-of-the-art machine learning algorithms, gradient-boosted regression trees (GBRT) are known to provide highly accurate predictions, as well as interpretable analysis based on the importance of features. Here, in a search for lead-free perovskites for use in solar cells, we applied the GBRT algorithm to a dataset of electronic structures for candidate halide double perovskites to predict heat of formation and bandgap. Statistical analysis of the selected features identifies design guidelines for the discovery of new lead-free perovskites.

The Poisson-Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson-Boltzmann type (PB n) equation with a small dielectric parameter 2 and nonlocal nonlinearity which takes into consideration of the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson-Nernst-Planck (PNP) system. Under Robin type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviors of one dimensional solutions of PB n equations as the parameter approaches to zero. In particular, we show that in case of electro-neutrality, i.e., α = β, solutions of 1-D PB n equations have the similar asymptotic behavior as those of 1-D PB equations. However, as α = β (local non-electroneutrality), solutions of 1-D PB n equations may have blow-up behavior which can not be found in 1-D PB equations. Such a difference between 1-D PB and PB n equations can also be verified by numerical simulations.

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In order to describe the dynamics of crowded ions (charged particles), we use an energetic variational approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity differences between ion species. Such a system has more complicated nonlinearities than the original PNP system but with the same equilibrium states. Using Galerkin's method and Schauder's fixed-point theorem, we develop a local existence theorem of classical solutions for the modified PNP system. Different dynamics (but same equilibrium states) between the original and modified PNP systems can be represented by numerical simulations using finite element method techniques.

Background: The aims of this study were to determine the predictive value of decision support analysis for the shock wave lithotripsy (SWL) success rate and to analyze the data obtained from patients who underwent SWL to assess the factors influencing the outcome by using machine learning methods. Methods: We retrospectively reviewed the medical records of 358 patients who underwent SWL for urinary stone (kidney and upper-ureter stone) between 2015 and 2018 and evaluated the possible prognostic features, including patient population characteristics, urinary stone characteristics on a non-contrast, computed tomographic image. We performed 80% training set and 20% test set for the predictions of success and mainly used decision tree-based machine learning algorithms, such as random forest (RF), extreme gradient boosting trees (XGBoost), and light gradient boosting method (LightGBM).Results: In machine learning analysis, the prediction accuracies for stone-free were 86.0, 87.5, and 87.9%, and those for one-session success were 78.0, 77.4, and 77.0% using RF, XGBoost, and LightGBM, respectively. In predictions for stone-free, LightGBM yielded the best accuracy and RF yielded the best one in those for one-session success among those methods. The sensitivity and specificity values for machine learning analytics are (0.74 to 0.78 and 0.92 to 0.93) for stone-free and (0.79 to 0.81 and 0.74 to 0.75) for one-session success, respectively. The area under curve (AUC) values for machine learning analytics are (0.84 to 0.85) for stone-free and (0.77 to 0.78) for one-session success and their 95% confidence intervals (CIs) are (0.730 to 0.933) and (0.673 to 0.866) in average of methods, respectively. Conclusions: We applied a selected machine learning analysis to predict the result after treatment of SWL for urinary stone. About 88% accurate machine learning based predictive model was evaluated. The importance of machine learning algorithm can give matched insights to domain knowledge on effective and influential factors for SWL success outcomes.