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Machine learning-based inverse materials discovery has attracted enormous attention recently due to its flexibility in dealing with black box models. Yet, many metaheuristic algorithms are not as widely applied to materials discovery applications as machine learning methods. There are ongoing challenges in applying different optimization algorithms to discover materials with single- or multi-elemental compositions and how these algorithms differ in mining the ideal materials. We comprehensively compare 11 different optimization algorithms for the design of single- and multi-elemental crystals with targeted properties. By maximizing the bulk modulus and minimizing the Fermi energy through perturbing the parameterized elemental composition representations, we estimated the unique counts of elemental compositions, mean density scan of the objectives space, mean objectives, and frequency distributed over the materials’ representations and objectives. We found that nature-inspired algorithms contain more uncertainties in the defined elemental composition design tasks, which correspond to their dependency on multiple hyperparameters. Runge–Kutta optimization (RUN) exhibits higher mean objectives, whereas Bayesian optimization (BO) displayed low mean objectives compared with other methods. Combined with materials count and density scan, we propose that BO strives to approximate a more accurate surrogate of the design space by sampling more elemental compositions and hence have lower mean objectives, yet RUN will repeatedly sample the targeted elemental compositions with higher objective values. Our work sheds light on the automated digital design of materials with single- and multi-elemental compositions and is expected to elicit future studies on materials optimization, such as composite and alloy design based on specific desired properties. 

To better fit the actual data, this paper will consider both spatio-temporal correlation and heterogeneity to build the model. In order to overcome the “curse of dimensionality” problem in the nonparametric method, we improve the estimation method of the single-index model and combine it with the correlation and heterogeneity of the spatio-temporal model to obtain a good estimation method. In this paper, assuming that the spatio-temporal process obeys the α mixing condition, a nonparametric procedure is developed for estimating the variance function based on a fully nonparametric function or dimensional reduction structure, and the resulting estimator is consistent. Then, a reweighting estimation of the parametric component can be obtained via taking the estimated variance function into account. The rate of convergence and the asymptotic normality of the new estimators are established under mild conditions. Simulation studies are conducted to evaluate the efficacy of the proposed methodologies, and a case study about the estimation of the air quality evaluation index in Nanjing is provided for illustration. 

We report a new deep learning message passing network that takes inspiration from Newton's equations of motion to learn interatomic potentials and forces. With the advantage of directional information from trainable force vectors, and physics-infused operators that are inspired by Newtonian physics, the entire model remains rotationally equivariant, and many-body interactions are inferred by more interpretable physical features. We test NewtonNet on the prediction of several reactive and non-reactive high quality ab initio data sets including single small molecules, a large set of chemically diverse molecules, and methane and hydrogen combustion reactions, achieving state-of-the-art test performance on energies and forces with far greater data and computational efficiency than other deep learning models. 

Abstract The generation of reference data for deep learning models is challenging for reactive systems, and more so for combustion reactions due to the extreme conditions that create radical species and alternative spin states during the combustion process. Here, we extend intrinsic reaction coordinate (IRC) calculations withab initioMD simulations and normal mode displacement calculations to more extensively cover the potential energy surface for 19 reaction channels for hydrogen combustion. A total of ∼290,000 potential energies and ∼1,270,000 nuclear force vectors are evaluated with a high quality range-separated hybrid density functional,ωB97X-V, to construct the reference data set, including transition state ensembles, for the deep learning models to study hydrogen combustion reaction.