Session Q15: Physical Symmetry-Aware Machine Learning of Interatomic Interactions and Properties of Materials

Atomic cluster expansion as a platform for constructing atomic scale models

Classical and machine learning interatomic potentials alike incorporate design choices that reflect the intuition of their authors and that are justified only a-posterioi by the performance of the model. Design choices comprise, for example, the form of the embedding function of an embedded atom potential or a specific angular dependence of a descriptor in a machine learning potential.

The atomic cluster expansion (ACE) [1-3] takes a different route. Based on the broad assumption of locality, it establishes a complete and orthonormal basis for the space of local atomic configurations. The ACE basis functions immediately comply with the basic symmetry requirements of atomic scale physics, they are invariant under translation, rotation, inversion and permutation of atoms. This enables the systematic expansion and convergence of atomic scale properties in analogy to quantum mechanics, where one is used to converging basis functions for the accurate representation of energies and forces. And the completeness enables ACE to represent common machine learning descriptors and potentials.

It is straightforward to include other properties than atomic energies in ACE, for example magnetic moments or charge transfer. By lifting the constraint of rotational invariance, vectorial or tensorial properties can be represented with a rotationally equivariant ACE. Furthermore, extensions to self-consistent models and non-local or semi-local interactions are possible and provide links to message passing networks. Finally, ACE is not limited to atoms but when applied to electrons recovers many-electron wavefunction representations.

 

[1] R. Drautz, Phys. Rev.  B99, 014104 (2019).

[2]  G. Dusson, M. Bachmayr, G. Csanyi, R. Drautz, S. Etter, C. van der Oord, and C. Ortner, (2020), arXiv:1911.03550v3.

[3] R. Drautz, Phys. Rev. B102, 024104 (2020).   

Equivariant Interatomic Potentials

Symmetry plays a central role in the representation of materials for the purpose of Machine Learning. In particular, all sensible representations must obey the symmetries of 3D space: translation, rotation, and inversion, in addition to permutation symmetry with respect to the labeling of atoms. Traditionally, representations have been constructed to possess invariance with respect to the above transformations. In this talk, I will discuss recent efforts to generalize invariance to the broader class of equivariant representations and demonstrate how this leads to a large increase in generalization accuracy and sample-efficiency of the learned models. The talk will then discuss the recently introduced Neural Equivariant Interatomic Potential (NequIP), an E(3)-equivariant Interatomic Potential that exhibits unprecedented accuracy and sample efficiency and outperforms invariant potentials with up to 1000x fewer reference data. I will discuss applications of NequIP to a diverse set of materials systems, including Li diffusion, amorphous structures, heterogeneous catalysis, and water. Finally, I will discuss our current theoretical understanding of the role of equivariance and explore connections with existing approaches, such as the atomic cluster expansion.   

Atomic Cluster Expansion Force Fields for Molecules

Machine Learning based force fields have revolutionised the modelling of materials at the atomistic scale. In this talk I will describe Atomic Cluster Expansion (ACE) which provides a systematic framework to derive a formally complete set of symmetric polynomial basis functions that can be used to build highly accurate and fast force fields. I will demonstrate that ACE force fields parametrised using regularised linear regression can compete in accuracy with most Gaussian Process and Neural Network based approaches. In particular, I will describe several applications of ACE to molecular systems where it shows excellent smooth and physical extrapolation to unseen parts of the Potential Energy Surface. Finally, I will demonstrate how the ACE framework can be extended to provide a unifying framework for machine learning potentials which includes message passing neural networks like SchNet and NequIP, Behler-Parinallo neural networks as well as the Gaussian Process regression based SOAP-GAP approaches.   

Designing molecular models by machine learning and experimental data

The last years have seen an immense increase in high-throughput and high-resolution technologies for experimental observation as well as high-performance techniques to

simulate molecular systems at a microscopic level, resulting in vast and ever-increasing amounts of high-dimensional data. However, experiments provide only a partial view of

macromolecular processes, and are limited in their temporal and spatial resolution. On the other hand, atomistic simulations are still not able to sample the conformation space of large complexes, thus leaving significant gaps in our ability to study molecular processes at a biologically relevant scale. We present our efforts to bridge these gaps, by exploiting the available data and using state-of-the-art machine-learning methods to design optimal coarse models for complex macromolecular systems. We show that it is possible to define

simplified molecular models to reproduce the essential information contained both in microscopic simulation and experimental measurement.