Performance and Cost Assessment of Machine Learning Interatomic Potentials.

Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors-atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the spectral neighbor analysis potential (SNAP) bispectrum components, and moment tensors-using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications

Applying Statistical Mechanics to Improve Computational Sampling Algorithms and Interatomic Potentials

In this dissertation the application of statistical mechanics is presented to improve classical simulated annealing and machine learning-based interatomic potentials. Classical simulated annealing is known to be among the most robust global optimization methods. Therefore, many variations of this method have been developed over the last few decades. This dissertation introduces simulated annealing with adaptive cooling and shows its efficiency with respect to the classical simulated annealing. Adaptive cooling simulated annealing makes use of the on-the-fly evaluation of the sta- tistical mechanical properties to adaptively adjust the cooling rate. In this case, the cooling rate is adaptively adjusted based on the instantaneous evaluations of the heat capacities, with the possible future extension to the density of states. Results are presented for Lennard-Jones clusters optimized by adaptive cooling sim- ulated annealing and the classical simulated annealing. The adaptive cooling approach proved to be more efficient than the classical simulated annealing. Statistical mechanics was also used to improve the quality and transferability of machine learning- based interatomic potentials. Machine learning (ML)-based interatomic potentials are currently garnering a lot of attention as they strive to achieve the accuracy of electronic structure methods at the computational cost of empirical potentials. Given their generic functional forms, the transferability of these potentials is highly dependent on the quality of the training set, the generation of which is a highly labor-intensive activity. Good training sets should at once contain a very diverse set of configurations while avoiding redundancies that incur cost without providing benefits. We formalize these requirements in a local entropy maximization framework and propose an automated sampling scheme to sample from this objective function. We show that this approach generates much more diverse training sets than unbiased sampling and is competitive with hand-crafted training sets[1]

PyXtal FF: a Python Library for Automated Force Field Generation

We present PyXtal FF, a package based on Python programming language, for developing machine learning potentials (MLPs). The aim of PyXtal FF is to promote the application of atomistic simulations by providing several choices of structural descriptors and machine learning regressions in one platform. Based on the given choice of structural descriptors (including the atom-centered symmetry functions, embedded atom density, SO4 bispectrum, and smooth SO3 power spectrum), PyXtal FF can train the MLPs with either the generalized linear regression or neural networks model, by simultaneously minimizing the errors of energy/forces/stress tensors in comparison with the data from the ab-initio simulation. The trained MLP model from PyXtal FF is interfaced with the Atomic Simulation Environment (ASE) package, which allows different types of light-weight simulations such as geometry optimization, molecular dynamics simulation, and physical properties prediction. Finally, we will illustrate the performance of PyXtal FF by applying it to investigate several material systems, including the bulk SiO2, high entropy alloy NbMoTaW, and elemental Pt for general purposes. Full documentation of PyXtal FF is available at https://pyxtal-ff.readthedocs.io.Comment: 13 pages, 4 figure