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.
Bibliographical noteFunding Information:
This research was partly supported by the Army Research Office (W911NF-14-1-0247) under the MURI program, and the National Science Foundation (NSF) under Grant Nos. DMR-1834251 and DMR-1931304. The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the results reported in this paper. M.W. thanks the University of Minnesota Doctoral Dissertation Fellowship for supporting his research.