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Many atomic descriptors are currently limited by their unfavourable scaling with the number of chemical elements $S$ e.g. the length of body-ordered descriptors, such as the Smooth Overlap of Atomic Positions (SOAP) power spectrum (3-body) and the Atomic Cluster Expansion (ACE) (multiple body-orders), scales as $(NS)^\nu$ where $\nu+1$ is the body-order and $N$ is the number of radial basis functions used in the density expansion. We introduce two distinct approaches which can be used to overcome this scaling for the SOAP power spectrum. Firstly, we show that the power spectrum is amenable to lossless compression with respect to both $S$ and $N$, so that the descriptor length can be reduced from $\mathcal{O}(N^2S^2)$ to $\mathcal{O}\left(NS\right)$. Secondly, we introduce a generalized SOAP kernel, where compression is achieved through the use of the total, element agnostic density, in combination with radial projection. The ideas used in the generalized kernel are equally applicably to any other body-ordered descriptors and we demonstrate this for the Atom Centered Symmetry Functions (ACSF). Finally, both compression approaches are shown to offer comparable performance to the original descriptor across a variety of numerical tests., Comment: 16 pages, 10 figures

The inverse problem of estimating the spatial distributions of elastic material properties from noisy strain measurements is ill-posed. However, it is still typically treated as an optimisation problem to maximise a likelihood function that measures the agreement between the measured and theoretically predicted strains. Here we propose an alternative approach employing Bayesian inference with Nested Sampling used to explore parameter space and compute Bayesian evidence. This approach not only aids in identifying the basis function set (referred to here as a model) that best describes the spatial material property distribution but also allows us to estimate the uncertainty in the predictions. Increasingly complex models with more parameters generate very high likelihood solutions and thus are favoured by a maximum likelihood approach. However, these models give poor predictions of the material property distributions with a large associated uncertainty as they overfit the noisy data. On the other hand, the Bayes’ factor peaks for a relatively simple model and indicates that this model is most appropriate even though its likelihood is comparatively low. Intriguingly, even for the appropriate model that has a unique maximum likelihood solution, the measurement noise is amplified to give large errors in the predictions of the maximum likelihood solution. By contrast, the mean of the posterior probability distribution reduces the effect of noise in the data and predicts the material properties with significantly higher fidelity. Simpler model selection criteria such as the Bayesian information criterion are shown to fail due to the non-Gaussian nature of the posterior distribution of the parameters. This makes accurate evaluation of the posterior distribution and the associated Bayesian evidence integral (by Nested Sampling or other means) imperative for this class of problems. The output of the Nested Sampling algorithm is also used to construct likelihood landscapes. These landscapes show the existence of multiple likelihood maxima when there is paucity of data and/or for overly complex models. They thus graphically illustrate the pitfalls in using optimisation methods to search for maximum likelihood solutions in such inverse problems.

One of the recurring anomalies in the hydrogen induced fracture of high strength steels is the apparent disconnect between their toughness and uniaxial tensile strength in identical hydrogen environments. Here we propose, supported by detailed atomistic and continuum calculations, that unlike macroscopic toughness, hydrogen-mediated tensile failure is a result of a fast-fracture mechanism. Specifically, we show that failure originates from the fast propagation of cleavage cracks that initiate from cavities that form around inclusions such as carbide particles. The failure process occurs in two stages. In stage-A, hydrides rapidly form around the roots of stressed notches on the cavity surfaces with hydrogen fed from the hydrogen gas within the cavity. These hydrides promote cleavage fracture with the cracks propagating at >100 ms^(-1) until the hydrogen gas in the cavity is exhausted. Predictions of this hydrogen-assisted crack growth mechanism are supported by atomistic calculations of binding energies, mobility barriers and molecular dynamics calculations of the fracture process. Typically, cracks grow by less than 1 μm via this hydrogen-assisted mechanism and thus insufficient to cause macroscopic fracture of the specimen. However, this stage is then followed by a stage-B process where these fast propagating cracks can continue to grow, now in the absence of hydrogen supply, given an appropriate level of remote tensile stress. This is surprising because the fracture energy is now that of Fe in the absence of H and cleavage fracture requires opening tractions on the order of 15 GPa to be generated. Thus, fracture is usually precluded due to plasticity around the crack-tip. Here we show via macroscopic continuum crack growth calculations in a rate dependent elastic-plastic solid with fracture modelled using a cohesive zone that cleavage is possible if the crack propagates fast enough. This is because strain-rates at the tips of fast propagating cracks are sufficiently high for the drag on the motion of dislocations resulting from phonon scattering to limit plasticity. This combined atomistic/continuum model is used to explain a host of well-established experimental observations including (but not limited to): (i) insensitivity of the strength to the concentration of trapped hydrogen; (ii) the extensive microcracking in addition to the final cleavage fracture event and (iii) the higher susceptibility of high strength steels to hydrogen embrittlement. Importantly, we also show that the stage-A hydrogen-assisted fracture process only occurs in certain crystallographic orientations with crack-tip plasticity processes, such as twinning, blunting cracks in other orientations. This inhibits the fast-fracture mechanism in a macroscopic toughness on a polycrystalline material and thus explains the apparent contradiction between the hydrogen-assisted macroscopic toughness and tensile strength of steels.

The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational cost and its scaling. Techniques based on machine learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations has remained a challenging goal. Here we present a Gaussian Approximation Potential for silicon that achieves this milestone, accurately reproducing density functional theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations that would be extremely expensive with a first principles electronic structure method, such as finite temperature phase boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential's accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material, and serves as a template for the development of such models in the future., Comment: 28 pages, 27 figures

Rett syndrome (RTT) is an early-onset neurodevelopmental disorder that almost exclusively affects girls and is totally disabling. Three genes have been identified that cause RTT: MECP2, CDKL5 and FOXG1. However, the etiology of some of RTT patients still remains unknown. Recently, next generation sequencing (NGS) has promoted genetic diagnoses because of the quickness and affordability of the method. To evaluate the usefulness of NGS in genetic diagnosis, we present the genetic study of RTT-like patients using different techniques based on this technology. We studied 1577 patients with RTT-like clinical diagnoses and reviewed patients who were previously studied and thought to have RTT genes by Sanger sequencing. Genetically, 477 of 1577 patients with a RTT-like suspicion have been diagnosed. Positive results were found in 30% by Sanger sequencing, 23% with a custom panel, 24% with a commercial panel and 32% with whole exome sequencing. A genetic study using NGS allows the study of a larger number of genes associated with RTT-like symptoms simultaneously, providing genetic study of a wider group of patients as well as significantly reducing the response time and cost of the study.

Titanium dioxide (titania, TiO$_2$) is a widely studied material with diverse applications. Here, we explore how pairwise and many-body descriptions of van der Waals dispersion interactions perform in atomistic modeling of the two most important TiO$_2$ polymorphs, rutile and anatase. In particular, we obtain an excellent description of both bulk structures from density-functional theory (DFT) computations with the many-body dispersion (MBD) method of Tkatchenko and co-workers coupled to an iterative Hirshfeld partitioning scheme ("Hirshfeld-I"). Beyond the bulk, we investigate the most important crystal surfaces, namely, rutile (110), (101), and (100) and anatase (101), (100), and (001). Dispersion has a highly anisotropic effect on the different ($\textit{hkl}$) surfaces; this directly changes the predicted nanocrystal morphology as determined from Wulff constructions. The periodic DFT+MBD method combined with Hirshfeld-I partitioning appears to be promising for future large-scale atomistic studies of this technologically important material.

We present a detailed quantum oscillation study of the Fermi surface of the recently discovered Yb-based heavy fermion superconductor β-YbAlB4. We compare the data, obtained at fields from 10 to 45 T, to band structure calculations performed using the local density approximation. Analysis of the data suggests that f holes participate in the Fermi surface up to the highest magnetic fields studied. We comment on the significance of these findings for the unconventional superconducting properties of this material. © 2009 The American Physical Society.

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS., Comment: 20 pages + supplementary information, 5 figures. preprint version; published version at https://www.nature.com/articles/s43586-022-00121-x

The plastic flow behavior of bcc transition metals up to moderate temperatures is dominated by the thermally activated glide of screw dislocations, which in turn is determined by the atomic-scale screw dislocation core structure and the associated kink-pair nucleation mechanism for glide. Modeling complex plasticity phenomena requires the simulation of many atoms and interacting dislocations and defects. These sizes are beyond the scope of first-principles methods and thus require empirical interatomic potentials. Especially for the technological important case of bcc Fe, existing empirical interatomic potentials yield spurious behavior. Here, the structure and motion of the screw dislocations in Fe are studied using a new Gaussian Approximation Potential (GAP) for bcc Fe, which has been shown to reproduce the potential energy surface predicted by density-functional theory (DFT) and many associated properties. The Fe GAP predicts a compact, non-degenerate core structure, a single-hump Peierls potential, and glide on {110}, consistent with DFT results. The thermally activated motion at finite temperatures occurs by the expected kink-pair nucleation and propagation mechanism. The stress-dependent enthalpy barrier for screw motion, computed using the nudged-elastic-band method, follows closely a form predicted by standard theories with a zero-stress barrier of ~1 eV, close to the experimental value of 0.84 eV, and a Peierls stress of ~2 GPa consistent with DFT predictions of the Peierls potential. A Gaussian Approximation Potential (GAP) can successfully reproduce the structure and motion of screw dislocations in iron. A team led by Francesco Maresca at the EPFL in Lausanne, Switzerland, used the recently developed GAP for iron to simulate aspects of screw dislocation behavior via both molecular statics and molecular dynamics simulations, and validated their results against density-functional theory calculations. The GAP for iron also successfully simulated kink-pair nucleation and screw dislocation glide along the {110} plane, while the stress-dependence of the enthalpy barrier for kink-pair nucleation was consistent with long-standing theories. This potential could be used to identify the atomic-scale origins of many other important plasticity phenomena such as dislocations interacting with radiation damage and cracks in iron and other body centered cubic materials.

We show that the Gaussian Approximation Potential (GAP) machine-learning framework can describe complex magnetic potential energy surfaces, taking ferromagnetic iron as a paradigmatic challenging case. The training database includes total energies, forces, and stresses obtained from density-functional theory in the generalized-gradient approximation, and comprises approximately 150,000 local atomic environments, ranging from pristine and defected bulk configurations to surfaces and generalized stacking faults with different crystallographic orientations. We find the structural, vibrational, and thermodynamic properties of the GAP model to be in excellent agreement with those obtained directly from first-principles electronic-structure calculations. There is good transferability to quantities, such as Peierls energy barriers, which are determined to a large extent by atomic configurations that were not part of the training set. We observe the benefit and the need of using highly converged electronic-structure calculations to sample a target potential energy surface. The end result is a systematically improvable potential that can achieve the same accuracy of density-functional theory calculations, but at a fraction of the computational cost.

Understanding the thermal properties of disordered systems is of fundamental importance for condensed matter physics - and it is of great relevance for practical applications as well. The manufacturing of window glass, the performance degradation of fiber-optics and the scalability of next-generation phase- change memories all depend on the thermal properties of amorphous solids. While macroscopic properties such as the thermal conductivity are usually well-characterised experimentally, their microscopic origin is often largely unknown. This is because the thermal properties of amorphous solids are determined by their vibrational (and possibly electronic) properties, which in turn depend upon the atomic-level structure. Hence there is a pressing need for atomistic simulations, which can in principle unravel the connection between microscopic structure and functional properties such as thermal conductivity. However, the large (long) length (time) scales involved are usually well beyond the reach of ab initio calculations. On the other hand, many interesting amorphous materials are characterised by a very complex structure. This often prevents the construction of classical interatomic potentials which would enable simulations on much larger (longer) length (time) scales – if compared to those achievable by first-principles simulations. One way to get past this deadlock is to harness machine-learning (ML) algorithms to build interatomic potentials: these can be nearly as computationally efficient as classical force fields for molecular dynamics simulations while retaining much of the accuracy of first-principles calculations. Here, we discuss the contribution of these ML-based potentials to our understanding of the thermal properties of amorphous solids. We focus on neural-network potentials (NNPs) and Gaussian approximation potentials (GAPs), two of the most widespread theoretical frameworks available to date. We review the work that has been devoted to investigate, via NNPs, the thermal properties of phase-change materials, a class of systems widely used in the context of non-volatile memories. In addition, we present recent results on the vibrational properties of amorphous carbon, studied via GAPs. In light of these results, we argue that ML-based potentials are among the best options available to further our understanding of the vibrational and thermal properties of complex amorphous solids.