In the past two decades, machine learning potentials (MLPs) have reached a level of maturity that now enables applications to large-scale atomistic simulations of a wide range of systems in chemistry, physics, and materials science. Different machine learning algorithms have been used with great success in the construction of these MLPs. In this review, we discuss an important group of MLPs relying on artificial neural networks to establish a mapping from the atomic structure to the potential energy. In spite of this common feature, there are important conceptual differences among MLPs, which concern the dimensionality of the systems, the inclusion of long-range electrostatic interactions, global phenomena like nonlocal charge transfer, and the type of descriptor used to represent the atomic structure, which can be either predefined or learnable. A concise overview is given along with a discussion of the open challenges in the field. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Atomic environment fingerprints are widely used in computational materials science, from machine learning potentials to the quantification of similarities between atomic configurations. Many approaches to the construction of such fingerprints, also called structural descriptors, have been proposed. In this work, we compare the performance of fingerprints based on the overlap matrix, the smooth overlap of atomic positions, Behler–Parrinello atom-centered symmetry functions, modified Behler–Parrinello symmetry functions used in the ANI-1ccx potential and the Faber–Christensen–Huang–Lilienfeld fingerprint under various aspects. We study their ability to resolve differences in local environments and in particular examine whether there are certain atomic movements that leave the fingerprints exactly or nearly invariant. For this purpose, we introduce a sensitivity matrix whose eigenvalues quantify the effect of atomic displacement modes on the fingerprint. Further, we check whether these displacements correlate with the variation of localized physical quantities such as forces. Finally, we extend our examination to the correlation between molecular fingerprints obtained from the atomic fingerprints and global quantities of entire molecules.

A central concern of molecular dynamics simulations are the potential energy surfaces that govern atomic interactions. These hypersurfaces define the potential energy of the system, and have generally been calculated using either pre-defined analytical formulas (classical) or quantum mechanical simulations (ab initio). The former can Gaussian approximation potential models for tungsten. Physical Review B, 90 (10):104108, 2014. 30 XW Zhou and RE Jones. Effects of cutoff functions of Tersoff potentials on molecular dynamics simulations of thermal transport. Modelling , et al. Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal processing magazine, 29(6):82-97, 2012. 32 B Yegnanarayana. Artificial neural networks. PHI Learning Pvt. Ltd., 2009. 33 Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436, 2015. 34 Balázs Csanád Csáji. Approximation with artificial neural networks. Master's thesis, Etvs Lornd University, Hungary, 2001. 35 Ajeevsing Bholoa, Steven D Kenny, and Roger Smith. A new approach to potential fitting using neural networks. Nuclear instruments and methods in physics research section B: Beam interactions with materials and atoms, 255(1):1-7, 2007. 36 Sönke Lorenz, Axel Groß, and Matthias Scheffler. Representing high-dimensional potentialenergy surfaces for reactions at surfaces by neural networks. Chemical Physics Letters, 395 (4-6):210-215, 2004. 37 Thomas B Blank, Steven D Brown, August W Calhoun, and Douglas J Doren. Neural network models of potential energy surfaces. The Journal of chemical physics, 103(10): 4129-4137, 1995. 38 Frederico V Prudente and JJ Soares Neto. The fitting of potential energy surfaces using neural networks. Application to the study of the photodissociation processes. Chemical physics letters, 287(5-6):585-589, 1998. 39 Ana Carla P Bittencourt, Frederico V Prudente, and José David M Vianna. The fitting of potential energy and transition moment functions using neural networks: transition probabilities in OH (A2Σ+ X2Π). Michael Isard, et al. Tensorflow: a system for large-scale machine learning. In OSDI, volume 16, pages 265-283, 2016. 47 John-Anders Stende. Constructing high-dimensional neural network potentials for molecular dynamics. Master's thesis, University of Oslo, Norway, 2017. 48 Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pages 249-256, 2010.

Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of electronic structure methods with the speed of classical interatomic potentials. A crucial component of a machine learning potential is the description of local atomic environments by some set of descriptors. These should ideally be invariant to the symmetries of the physical system, twice-differentiable with respect to atomic positions (including when an atom leaves the environment), and complete to allow the atomic environment to be reconstructed up to symmetry.The stronger condition of optimal completeness requires that the condition for completeness be satisfied with the minimum possible number of descriptors. Evidence is provided that an updated version of the recently proposed Spherical Bessel (SB) descriptors satisfies the first two properties and a necessary condition for optimal completeness. The Smooth Overlap of Atomic Position (SOAP) descriptors and the Zernike descriptors are natural counterparts of the SB descriptors and are included for comparison. The standard construction of the SOAP descriptors is shown to not satisfy the condition for optimal completeness, and moreover is found to be an order of magnitude slower to compute than the SB descriptors.

Thermal transport in a water-Cu nanocolloid system was investigated using equilibrium molecular dynamics. A systematic analysis of the Green-Kubo calculations is presented to clarify the effect of simulation parameters. Several sources of error were identified and quantified for the thermal conductivity estimations, and the effect of the base fluid potential was investigated. Simulations were carried out with a single copper particle for different diameters and water potentials, and thermal enhancements exceeding both theoretical and experimental results were observed in parallel with some other studies in the literature. The anomalous Green-Kubo thermal enhancement results could be explained by the interfacial dynamics and the neglect of calibrating the interaction potential to satisfy the physically-observed energy flow at the interface.