Neural network aided development of a semi-empirical interatomic potential for titanium

Abstract Artificial neural networks, utilizing machine learning techniques to uncover subtle and complex patterns in big data problems, are able to condense large amounts of computationally expensive density functional theory and ab initio results into classical force field potentials. However, in order to produce a computationally efficient network, with minimal network architecture, a structural fingerprint whose components are highly correlated to the per atom energy is necessary. In this paper, we demonstrate the effectiveness a structural fingerprint motivated by the highly successful MEAM formalism by creating an artificial neural network containing a single hidden layer of 20 nodes which provides a semi-empirical force field potential for elemental titanium. This potential is suitable for dynamic calculations of α -, β -, and ω -titanium at a variety of temperatures. This potential is able to achieve a number of results in agreement with DFT calculations which surpass classical potential formalisms with comparable computational performance.