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Register a new userSymmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
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Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that can be used to perform machine-learning of tensorial properties of arbitrary rank for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions (SOAP) kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous electrical response of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.
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A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known inter-atomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double anti-ferromagnetic materials, as well as, charge density waves induced by a non-uniform spin structure are given. In the final parts, a set of coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and damped driven mechanical oscillator for the ...
Amorphous silicon (a-Si) is a widely studied non-crystalline material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained by harnessing the power of machine-learning algorithms to create interatomic potentials. Our best a-Si network is obtained by cooling from the melt in molecular-dynamics simulations, at a rate of 10$^{11}$ K/s (that is, on the 10 ns timescale). This structure shows a defect concentration of below 2% and agrees with experiments regarding excess energies, diffraction data, as well as $^{29}$Si solid-state NMR chemical shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4,096-atom system which correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with experiments to date. Our study demonstrates the broader impact of machine-learning interatomic potentials for elucidating accurate structures and properties of amorphous functional materials.
We devise automated workflows for the calculation of Helmholtz and Gibbs free energies and their temperature and pressure dependence and provide the corresponding computational tools. We employ non-equilibrium thermodynamics for evaluating the free energy of solid and liquid phases at a given temperature and reversible scaling for computing free energies over a wide range of temperatures, including the direct integration of $P$-$T$ coexistence lines. By changing the chemistry and the interatomic potential, alchemical and upscaling free energy calculations are possible. Several examples illustrate the accuracy and efficiency of our implementation.
In this work, we discuss use of machine learning techniques for rapid prediction of detonation properties including explosive energy, detonation velocity, and detonation pressure. Further, analysis is applied to individual molecules in order to explore the contribution of bonding motifs to these properties. Feature descriptors evaluated include Morgan fingerprints, E-state vectors, a custom sum over bonds descriptor, and coulomb matrices. Algorithms discussed include kernel ridge regression, least absolute shrinkage and selection operator (LASSO) regression, Gaussian process regression, and the multi-layer perceptron (a neural network). Effects of regularization, kernel selection, network parameters, and dimensionality reduction are discussed. We determine that even when using a small training set, non-linear regression methods may create models within a useful error tolerance for screening of materials.
Quantitative descriptions of the structure-thermal property correlation have been a bottleneck in designing materials with superb thermal properties. In the past decade, the first-principles phonon calculations using density functional theory and the Boltzmann transport equation have become a common practice for predicting the thermal conductivity of new materials. However, first-principles calculations are too costly for high-throughput material screening and multi-scale structural design. First-principles calculations also face several fundamental challenges in modeling thermal transport properties, e.g., of crystalline materials with defects, of amorphous materials, and for materials at high temperatures. In the past five years, machine learning started to play a role in solving these challenges. This review provides a comprehensive summary and discussion on the state-of-the-art, future opportunities, and the remaining challenges in implementing machine learning for studying thermal conductivity. After an introduction to the working principles of machine learning and descriptors of material structures, recent research using machine learning to study thermal transport is discussed. Three major applications of machine learning for predicting thermal properties are discussed. First, machine learning is applied to solve the challenges in modeling phonon transport of crystals with defects, in amorphous materials, and at high temperatures. Machine learning is used to build high-fidelity interatomic potentials to bridge the gap between first-principles calculations and molecular dynamics simulations. Second, machine learning can be used to study the correlation between thermal conductivity and other properties for high-throughput materials screening. Finally, machine learning is a powerful tool for structural design to achieve target thermal conductance or thermal conductivity.
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