Deep Neural Network Potentials for Atomistic Simulations

## Abstract

Computer modeling it is today a vital part of material science. One of the most common methods for computational modeling of materials is density functional theory (DFT). In DFT, the interactions between atoms (the potential energy surface) is modeled using quantum mechanics making it a very powerful method. However, solving the Schrödinger equation is numerically demanding which makes DFT very computationally expensive. To study large systems (millions of atoms) and long timescales (microseconds) one would today rely on force field (FF) methods. These are empirical methods where the interactions between atoms are described by parameterized mathematical expressions which are “user” defined. Meaning that they are derived from theory or purely empirical. This eliminates the need to solve the Schrödinger equation making FF methods significantly faster than DFT. Of course, FF methods have their own drawbacks such as low accuracy and poor generalizability.
Machine learning can be used to combine the accuracy and generalizability of DFT with the low computational cost (high speed) of FF methods. By training deep neural network potentials (NNPs) on data (atomic structures, potential energies, and forces) from DFT calculations the NNPs learns the interactions between atoms (the potential energy surface). Thus, the NNPs can predict potential energies and forces of atomic structures with DFT accuracy but at the speed of FF methods. NNPs have a much better ability to correctly describe the potential energy surface of an atomic system compared to FF methods. Since the NNPs does not rely on “user” defined fixed mathematical expressions, but instead learns the mathematical description of the potential energy surface based on the training data [1]. It has been shown that NNPs are able to predict energies and forces with accuracies close to DFT [2,3] and that such trained DNN potentials can be used to perform atomistic simulations [3,4,5]. The field of DNN potentials is still in its infancy and there are many questions yet to be answered. This is a collaborative research project between Korea (Institute for Basic Science), Germany (Chemnitz University of Technology) and Sweden (Luleå University of Technology).
[1] J. Behler, Angew. Chem. Int. Ed. Engl. 56, 12828 (2017).
[2] A. Khorshidi and A. A. Peterson, Computer Physics Communications 207, 310 (2016).
[3] D. Hedman, T. Rothe, G. Johansson, F. Sandin, J. A. Larsson and Y. Miyamoto, Carbon Trends 3, 100027 (2021).
[4] J. Magnusson, Training Neural Network Potentials for Atomistic Calculations on Carbon Materials: An initial study on diamond structures (Luleå University of Technology, 2018).
[5] J. Carlstedt and V. Rönnerfjäll, Examining Deep Neural Network Potentials for use in Atomistic Simulations of Carbon Nanotube Growth (Luleå University of Technology, 2019).