IMSE Seminar with Richard Hennig on Machine Learning
Machine learning can identify new symbolic expressions that describe physical relationships and provide surrogate models that accelerate the search for new materials. I will present an example for each type of learning: (i) the data-driven discovery of the functional form of the superconducting critical temperature and (ii) the learning of effective many-body potentials for the accelerated exploration of materials' energy landscapes.
First, predicting the critical temperature, Tc, of superconductors is a notoriously challenging task, even for electron-phonon systems. We build on earlier efforts by McMillan, Allen, and Dynes to model Tc from various measures of the phonon spectrum and the electron-phonon interaction by using machine learning algorithms. Specifically, we apply symbolic regression to a dataset of calculated materials data augmented by a generalized Einstein model to identify a new, physically interpretable equation for Tc as a function of a small number of physical quantities. The figure above shows the the machine-learned equation and illustrates that our model improves upon the Allen-Dynes fit and generalizes to superconducting materials with higher Tc, such as the hydrides H3S and LaH10. By incorporating physical insights and constraints into a data-driven approach, we demonstrate that machine-learning methods can identify the relevant physical quantities and obtain predictive equations using small but high-quality datasets [1,2].
Description automatically generated Second, crystal structure predictions and all-atom dynamics simulations have become indispensable quantitative tools in chemistry, physics, and materials science, but large systems and long simulation times remain elusive due to the trade-off between computational efficiency and predictive accuracy. To address this challenge, we combine effective many-body potentials in a cubic B-spline basis with regularized linear regression to obtain machine-learning potentials that are physically interpretable, sufficiently accurate for applications, and as fast as the fastest traditional empirical potentials [3]. We demonstrate the exact retrieval of two and three-body potentials from data and obtain reasonable predictive accuracy for data from ab-initio simulations. We show that these ultra-fast potentials are two to four orders of magnitude faster than state-of-the-art machine-learning potentials but close in accuracy and enable accurate all-atom dynamics simulations of large atomistic systems over long timescales. We illustrate that these potentials can accurately describe a range of materials from close-packed metals and intermetallic to the more open structures of semiconductors. These two applications illustrate the power of machine learning to accelerate the discovery and design of innovative materials.
[1] Machine learning of superconducting critical temperature from Eliashberg theory. S. R. Xie, Y. Quan, A. C. Hire, B. Deng, J. M. DeStefano, I. Salinas, U. S. Shah, L. Fanfarillo, J. Lim, J. Kim, G. R. Stewart, J. J. Hamlin, P. J. Hirschfeld, and R. G. Hennig, npj Computational Materials 8, 1 (2022), doi:10.1038/s41524-021-00666-7.
[2] Functional Form of the Superconducting Critical Temperature from Machine Learning. S. R. Xie, G. R. Stewart, J. J. Hamlin, P. J. Hirschfeld, and R. G. Hennig, Phys. Rev. B 100, 174513 (2019), doi:10.1103/PhysRevB.100.174513.
[3] Ultra-fast interpretable machine-learning potentials. S. R. Xie, M. Rupp, and R. G. Hennig, arXiv:2110.00624 (2020), doi:10.48550/arXiv.2110.00624.
Professor Hennig received his Diploma in Physics at the University of Göttingen in 1996 and his Ph.D. in Physics from Washington University in St. Louis in 2000. After working as a postdoctoral researcher and research scientist at Ohio State University, he joined the faculty of the Department of Materials Science and Engineering at Cornell in 2006 as an Assistant Professor. In 2014 he moved to the University of Florida where he is the Alumni Professor of Materials Science and Engineering and the Associate Director, Quantum Theory Project.