ACEpotentials.jl: A Julia implementation of the atomic cluster expansion.

We introduce ACEpotentials.jl, a Julia-language software package that constructs interatomic potentials from quantum mechanical reference data using the Atomic Cluster Expansion [R. Drautz, Phys. Rev. B 99, 014104 (2019)]. As the latter provides a complete description of atomic environments, including invariance to overall translation and rotation as well as permutation of like atoms, the resulting potentials are systematically improvable and data efficient. Furthermore, the descriptor's expressiveness enables use of a linear model, facilitating rapid evaluation and straightforward application of Bayesian techniques for active learning. We summarize the capabilities of ACEpotentials.jl and demonstrate its strengths (simplicity, interpretability, robustness, performance) on a selection of prototypical atomistic modelling workflows.

Tensor-Reduced Atomic Density Representations.

Density-based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modeling, and the visualization and analysis of material datasets. The standard mechanism used to incorporate chemical element information is to create separate densities for each element and form tensor products between them. This leads to a steep scaling in the size of the representation as the number of elements increases. Graph neural networks, which do not explicitly use density representations, escape this scaling by mapping the chemical element information into a fixed dimensional space in a learnable way. By exploiting symmetry, we recast this approach as tensor factorization of the standard neighbour-density-based descriptors and, using a new notation, identify connections to existing compression algorithms. In doing so, we form compact tensor-reduced representation of the local atomic environment whose size does not depend on the number of chemical elements, is systematically convergable, and therefore remains applicable to a wide range of data analysis and regression tasks.

Hyperactive learning for data-driven interatomic potentials.

Data-driven interatomic potentials have emerged as a powerful tool for approximating ab initio potential energy surfaces. The most time-consuming step in creating these interatomic potentials is typically the generation of a suitable training database. To aid this process hyperactive learning (HAL), an accelerated active learning scheme, is presented as a method for rapid automated training database assembly. HAL adds a biasing term to a physically motivated sampler (e.g. molecular dynamics) driving atomic structures towards uncertainty in turn generating unseen or valuable training configurations. The proposed HAL framework is used to develop atomic cluster expansion (ACE) interatomic potentials for the AlSi10 alloy and polyethylene glycol (PEG) polymer starting from roughly a dozen initial configurations. The HAL generated ACE potentials are shown to be able to determine macroscopic properties, such as melting temperature and density, with close to experimental accuracy.

Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions" [J. Chem. Phys. 156, 034302 (2022)].

The "quasi-constant" smooth overlap of atomic position and atom-centered symmetry function fingerprint manifolds recently discovered by Parsaeifard and Goedecker [J. Chem. Phys. 156, 034302 (2022)] are closely related to the degenerate pairs of configurations, which are known shortcomings of all low-body-order atom-density correlation representations of molecular structures. Configurations that are rigorously singular-which we demonstrate can only occur in finite, discrete sets and not as a continuous manifold-determine the complete failure of machine-learning models built on this class of descriptors. The "quasi-constant" manifolds, on the other hand, exhibit low but non-zero sensitivity to atomic displacements. As a consequence, for any such manifold, it is possible to optimize model parameters and the training set to mitigate their impact on learning even though this is often impractical and it is preferable to use descriptors that avoid both exact singularities and the associated numerical instability.

Body-Ordered Approximations of Atomic Properties.

We show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energy has an exponential rate of convergence both at finite Fermi-temperature as well as for insulators at zero Fermi-temperature. We discuss potential consequences of this observation for modelling the potential energy landscape, as well as for solving the electronic structure problem.

Linear Atomic Cluster Expansion Force Fields for Organic Molecules: Beyond RMSE.

We demonstrate that fast and accurate linear force fields can be built for molecules using the atomic cluster expansion (ACE) framework. The ACE models parametrize the potential energy surface in terms of body-ordered symmetric polynomials making the functional form reminiscent of traditional molecular mechanics force fields. We show that the four- or five-body ACE force fields improve on the accuracy of the empirical force fields by up to a factor of 10, reaching the accuracy typical of recently proposed machine-learning-based approaches. We not only show state of the art accuracy and speed on the widely used MD17 and ISO17 benchmark data sets, but we also go beyond RMSE by comparing a number of ML and empirical force fields to ACE on more important tasks such as normal-mode prediction, high-temperature molecular dynamics, dihedral torsional profile prediction, and even bond breaking. We also demonstrate the smoothness, transferability, and extrapolation capabilities of ACE on a new challenging benchmark data set comprised of a potential energy surface of a flexible druglike molecule.

Physics-Inspired Structural Representations for Molecules and Materials.

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

Local invertibility and sensitivity of atomic structure-feature mappings.

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety of representations that can be used to convert them into a finite set of symmetric descriptors or features. Methods: Here, we analyze the sensitivity of the mapping to atomic displacements, using a singular value decomposition of the Jacobian of the transformation to quantify the sensitivity for different configurations, choice of representations and implementation details.  Results: We show that the combination of symmetry and smoothness leads to mappings that have singular points at which the Jacobian has one or more null singular values (besides those corresponding to infinitesimal translations and rotations). This is in fact desirable, because it enforces physical symmetry constraints on the values predicted by regression models constructed using such representations. However, besides these symmetry-induced singularities, there are also spurious singular points, that we find to be linked to the incompleteness of the mapping, i.e. the fact that, for certain classes of representations, structurally distinct configurations are not guaranteed to be mapped onto different feature vectors. Additional singularities can be introduced by a too aggressive truncation of the infinite basis set that is used to discretize the representations. Conclusions: These results exemplify the subtle issues that arise when constructing symmetric representations of atomic structures, and provide conceptual and numerical tools to identify and investigate them in both benchmark and realistic applications.

Incompleteness of Atomic Structure Representations.

Many-body descriptors are widely used to represent atomic environments in the construction of machine-learned interatomic potentials and more broadly for fitting, classification, and embedding tasks on atomic structures. There is a widespread belief in the community that three-body correlations are likely to provide an overcomplete description of the environment of an atom. We produce several counterexamples to this belief, with the consequence that any classifier, regression, or embedding model for atom-centered properties that uses three- (or four)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centered contributions mitigates the impact of this fundamental deficiency-explaining the success of current "machine-learning" force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.

Sensitivity and dimensionality of atomic environment representations used for machine learning interatomic potentials.

Faithfully representing chemical environments is essential for describing materials and molecules with machine learning approaches. Here, we present a systematic classification of these representations and then investigate (i) the sensitivity to perturbations and (ii) the effective dimensionality of a variety of atomic environment representations and over a range of material datasets. Representations investigated include atom centered symmetry functions, Chebyshev Polynomial Symmetry Functions (CHSF), smooth overlap of atomic positions, many-body tensor representation, and atomic cluster expansion. In area (i), we show that none of the atomic environment representations are linearly stable under tangential perturbations and that for CHSF, there are instabilities for particular choices of perturbation, which we show can be removed with a slight redefinition of the representation. In area (ii), we find that most representations can be compressed significantly without loss of precision and, further, that selecting optimal subsets of a representation method improves the accuracy of regression models built for a given dataset.

A preconditioning scheme for minimum energy path finding methods.

Popular methods for identifying transition paths between energy minima, such as the nudged elastic band and string methods, typically do not incorporate potential energy curvature information, leading to slow relaxation to the minimum energy path for typical potential energy surfaces encountered in molecular simulation. We propose a preconditioning scheme which, combined with a new adaptive time step selection algorithm, substantially reduces the computational cost of transition path finding algorithms. We demonstrate the improved performance of our approach in a range of examples including vacancy and dislocation migration modeled with both interatomic potentials and density functional theory.

Preconditioners for the geometry optimisation and saddle point search of molecular systems.

A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to construct a sparse preconditioner matrix. The construction requires only the computation of the gradient of the corresponding molecular mechanical terms that are already available in popular force field software packages. For molecular crystals, the preconditioner can be combined straightforwardly with the exponential preconditioner recently introduced for periodic systems. The efficiency is demonstrated on several systems using empirical, semiempirical and ab initio potential energy surfaces.

Polytypism in the ground state structure of the Lennard-Jonesium.

We present a systematic study of the stability of nineteen different periodic structures using the finite range Lennard-Jones potential model discussing the effects of pressure, potential truncation, cutoff distance and Lennard-Jones exponents. The structures considered are the hexagonal close packed (hcp), face centred cubic (fcc) and seventeen other polytype stacking sequences, such as dhcp and 9R. We found that at certain pressure and cutoff distance values, neither fcc nor hcp is the ground state structure as previously documented, but different polytypic sequences. This behaviour shows a strong dependence on the way the tail of the potential is truncated.

Intraindividual comparison between femtosecond laser-assisted and conventional cataract surgery.

PURPOSE: To compare the safety and efficacy between femtosecond laser-assisted cataract surgery using the Victus laser system and conventional cataract surgery. SETTING: Department of Ophthalmology, Kepler University Hospital, Linz, Austria. DESIGN: Prospective randomized case series. METHODS: Both eyes of patients with age-related cataract were randomized to conventional cataract surgery or femtosecond laser-assisted cataract surgery, both with intraocular lens (IOL) implantation. Postoperative follow-up was at 1 day, 1 week, 1 month, 3 months, and 6 months and comprised corrected distance visual acuity, endothelial cell density (ECD), central corneal thickness (CCT), and central retinal thickness. The main outcomes were intraoperative and postoperative complications and the effective phacoemulsification time (EPT). Intraocular lens and capsulotomy centration were evaluated using retroillumination slitlamp photography. RESULTS: The study enrolled 50 patients. No intraoperative complications occurred in either group. The ECD, CCT, and central retinal thickness were similar between the groups at all follow-up examinations (P > .05). The EPT was not statistically significantly different between the groups (P = .22). The IOL centration was similar between the groups (P = .93). CONCLUSION: Femtosecond laser-assisted and conventional cataract surgery using the mentioned system were equally safe and effective.

A universal preconditioner for simulating condensed phase materials.

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

Complement factor H Y402H gene polymorphism and response to intravitreal bevacizumab in exudative age-related macular degeneration.

PURPOSE: To determine whether different complement factor H (CFH) genotypes play a role in treatment of age-related macular degeneration (AMD) with intravitreal bevacizumab. METHODS: In this prospective study, we included 197 patients with exudative AMD and treated with 1.25 mg intravitreal bevacizumab at 6-week intervals until choroidal neovascularization (CNV) was no longer active. In all patients, ophthalmological examinations, visual acuity, optical coherence tomography (OCT), fundus photography and fluorescein angiography were performed. Single nucleotide polymorphism (SNP) genotyping was performed using restriction fragment length polymorphism (RFLP) analysis of polymerase chain reaction (PCR) products. RESULTS: Age, gender and baseline mean visual acuity were similar among the three CFH genotypes. There was no significant difference in underlying lesion type of CNV, lesion size, number of injections or macula thickness. When examining the effect of genotype on post-treatment visual acuities, we observed a significant worse outcome for distance and reading visual acuity in the CFH 402HH genotype group. The number of patients who lost 3 or more lines in distance and reading visual acuity testing was significantly higher in the CFH 402HH (41%, 46%) genotype group than in patients with the CFH 402YY (28%, 26%) and CFH 402YH (26%, 24%) genotype. CONCLUSIONS: In addition to the higher risk for exudative AMD in patients with the CFH 402HH genotype that was found in previous studies, our results show that the CFH 402HH genotype also correlates with lower visual acuity outcome after treatment with bevacizumab, suggesting that pharmacogenetics of CFH plays a role in response to treatment of wet AMD.