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1. Uncertainty quantification in molecular simulations with dropout neural network potentials

   https://doi.org/10.1038/s41524-020-00390-8  

   Wen, Mingjian ; Tadmor, Ellad B. ( August 2020 , npj Computational Materials)

   Machine learning interatomic potentials (IPs) can provide accuracy close to that of first-principles methods, such as density functional theory (DFT), at a fraction of the computational cost. This greatly extends the scope of accurate molecular simulations, providing opportunities for quantitative design of materials and devices on scales hitherto unreachable by DFT methods. However, machine learning IPs have a basic limitation in that they lack a physical model for the phenomena being predicted and therefore have unknown accuracy when extrapolating outside their training set. In this paper, we propose a class of Dropout Uncertainty Neural Network (DUNN) potentials that provide rigorous uncertainty estimates that can be understood from both Bayesian and frequentist statistics perspectives. As an example, we develop a DUNN potential for carbon and show how it can be used to predict uncertainty for static and dynamical properties, including stress and phonon dispersion in graphene. We demonstrate two approaches to propagate uncertainty in the potential energy and atomic forces to predicted properties. In addition, we show that DUNN uncertainty estimates can be used to detect configurations outside the training set, and in some cases, can serve as a predictor for the accuracy of a calculation.

    

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2. A deep learning framework to emulate density functional theory

   https://doi.org/10.1038/s41524-023-01115-3  

   del Rio, Beatriz G. ; Phan, Brandon ; Ramprasad, Rampi ( August 2023 , npj Computational Materials)

   Density functional theory (DFT) has been a critical component of computational materials research and discovery for decades. However, the computational cost of solving the central Kohn–Sham equation remains a major obstacle for dynamical studies of complex phenomena at-scale. Here, we propose an end-to-end machine learning (ML) model that emulates the essence of DFT by mapping the atomic structure of the system to its electronic charge density, followed by the prediction of other properties such as density of states, potential energy, atomic forces, and stress tensor, by using the atomic structure and charge density as input. Our deep learning model successfully bypasses the explicit solution of the Kohn-Sham equation with orders of magnitude speedup (linear scaling with system size with a small prefactor), while maintaining chemical accuracy. We demonstrate the capability of this ML-DFT concept for an extensive database of organic molecules, polymer chains, and polymer crystals.

    

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3. Highly transferable atomistic machine-learning potentials from curated and compact datasets across the periodic table

   https://doi.org/10.1039/D3DD00046J  

   Andolina, Christopher M. ; Saidi, Wissam A. ( August 2023 , Digital discovery)

   Machine learning atomistic potentials (MLPs) trained using density functional theory (DFT) datasets allow for the modeling of complex material properties with near-DFT accuracy while imposing a fraction of its computational cost.

    

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4. Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

   https://doi.org/10.3390/app11052395  

   Kirchner-Hall, Nicole E. ; Zhao, Wayne ; Xiong, Yihuang ; Timrov, Iurii ; Dabo, Ismaila ( March 2021 , Applied Sciences)

   null (Ed.)

   Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initio U parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost. 

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5. An accurate machine learning calculator for the lithium-graphite system

   https://doi.org/10.1088/2515-7655/abc96f  

   Babar, Mohammad ; Parks, Holden L. ; Houchins, Gregory ; Viswanathan, Venkatasubramanian ( December 2020 , Journal of Physics: Energy)

   Machine-learning potentials are accelerating the development of energy materials, especially in identifying phase diagrams and other thermodynamic properties. In this work, we present a neural network potential based on atom-centered symmetry function descriptors to model the energetics of lithium intercalation into graphite. The potential was trained on a dataset of over 9000 diverse lithium–graphite configurations that varied in applied stress and strain, lithium concentration, lithium–carbon and lithium–lithium bond distances, and stacking order to ensure wide sampling of the potential atomic configurations during intercalation. We calculated the energies of these structures using density functional theory (DFT) through the Bayesian error estimation functional with van der Waals correlation exchange-correlation functional, which can accurately describe the van der Waals interactions that are crucial to determining the thermodynamics of this phase space. Bayesian optimization, as implemented inDragonfly, was used to select optimal set of symmetry function parameters, ultimately resulting in a potential with a prediction error of 8.24 meV atom⁻¹on unseen test data. The potential can predict energies, structural properties, and elastic constants at an accuracy comparable to other DFT exchange-correlation functionals at a fraction of the computational cost. The accuracy of the potential is also comparable to similar machine-learned potentials describing other systems. We calculate the open circuit voltage with the calculator and find good agreement with experiment, especially in the regimex ≥ 0.3, forxin Li_xC₆. This study further illustrates the power of machine learning potentials, which promises to revolutionize design and optimization of battery materials.

    

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