Machine-learning interatomic potentials from a users perspective: A comparison of accuracy, speed and data efficiency

TL;DR

It is found that nonlinear ACE and the equivariant, message-passing graph neural networks NequIP and MACE form the Pareto front in the accuracy vs. computational cost trade-off in the Al–Cu–Zr system, while NequIP outperforms them for Si–O.

Abstract

Machine learning interatomic potentials (MLIPs) have massively changed the field of atomistic modeling. They enable the accuracy of density functional theory in large-scale simulations while being nearly as fast as classical interatomic potentials. Over the last few years, a wide range of different types of MLIPs have been developed, but it is often difficult to judge which approach is the best for a given problem setting. For the case of structurally and chemically complex solids, namely Al-Cu-Zr and Si-O, we benchmark a range of machine learning interatomic potential approaches, in particular, the Gaussian approximation potential (GAP), high-dimensional neural network potentials (HDNNP), moment tensor potentials (MTP), the atomic cluster expansion (ACE) in its linear and nonlinear version, neural equivariant interatomic potentials (NequIP), Allegro, and MACE. We find that nonlinear ACE and the equivariant, message-passing graph neural networks NequIP and MACE form the Pareto front in the accuracy vs. computational cost trade-off. In case of the Al-Cu-Zr system we find that MACE and Allegro offer the highest accuracy, while NequIP outperforms them for Si-O. Furthermore, GPUs can massively accelerate the MLIPs, bringing them on par with and even ahead of non-accelerated classical interatomic potentials (IPs) with regards to accessible timescales. Finally, we explore the extrapolation behavior of the corresponding potentials, probe the smoothness of the potential energy surfaces, and finally estimate the user friendliness of the corresponding fitting codes and molecular dynamics interfaces.

Figures (9)

• Figure 1: The main ingredients of a MLIP. (1) A database is needed connecting the point cloud of atomic configurations and learnable properties of interest (i.e. energies and forces). (2) A representation of these atomic configurations is needed, which is translationally and rotationally invariant or equivariant. Here, two different types are established. The descriptor based approach takes a descriptor vector as fingerprint of each local environment in a given cutoff radius. Graph networks messages, in contrast, are transmitted between neighboring atoms, providing information about their environment to those neighbors. Using multiple message passing iterations allows these approaches to have a higher effective cutoff and therefore, to include additional semi-local information. This is depicted by the graph network on the right in (2), where the blue atom can receive information about atoms that would otherwise only be seen by the green atom. (3) The corresponding representation techniques are combined with a variation of different machine-learning techniques to relate these representations with local and global properties of the given point cloud. As a feature, various machine-learning techniques allow to assess a uncertainty for estimating the reliability of a potential in certain parts of configurational space. Figure inspired by Ref. deringerMachineLearningInteratomic2019 and adapted to show graph neural networks.
• Figure 2: Accuracy vs. computational cost of the assessed MLIP: Shown are the MAE of energy and forces vs. runtime per atom and time step. The top row shows the Al-Cu-Zr system, the lower row the Si-O system. In the case of Al-Cu-Zr the GAP are trained with only 10% of the training data, because of their large RAM requirement during the process, indicated by the white pattern in plot marks. For the Al-Cu-Zr system the speed of the widely used Cu-Zr EAM potential by Mendelev is additionally indicated by the gray line mendelevDevelopmentSemiempiricalPotential2019. Speed measurements have been performed on the Horeka supercomputer on a single core of a Intel Xeon Platinum 8368 processor. Amorphous systems with sizes of 1372 and 768 atoms were used for Al-Cu-Zr and Si-O, respectively. Due to the larger size of the Al-Cu-Zr training dataset and the higher chemical complexity and therefore higher computational costs of fitting less fits are available. The potentials we used in our later tests are marked by a cross.
• Figure 3: GPU performance for the assessed MLIP for silica. Speed measurements have been performed on the Horeka supercomputer on 1 Nvidia A100 GPU. The gray shapes correspond to the computational costs on a single CPU core (see \ref{['fig:AccuracyCostCPU']}).
• Figure 4: Energy deviation as function of system temperature calculated for various MLIP in NVE simulations over 100ps. A low energy loss is indicating a smooth PES. Note the different y-scales in both graphs. We used a time step of 1 fs for all simulations. Indeed, for simulations at higher temperatures a lower time step might be necessary to still conserve the energy. In case of silica, three MLIP failed at certain temperatures (MACE, linear ACE, HDNNP), which indicates a noisy PES at higher energy levels. The highest working temperatures for these potentials are indicated by a cross.
• Figure 5: Learning curve of tested MLIP. For Al-Cu-Zr no GAP is shown, as fitting was possible only with 10% of the training data due to memory issues, as described previously. The errors shown are referring to the test set.