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The Open Databases Integration for Materials Design (OPTIMADE) application programming interface (API) empowers users with holistic access to a growing federation of databases, enhancing the accessibility and discoverability of materials and chemical data. Since the first release of the OPTIMADE specification (v1.0), the API has undergone significant development, leading to the upcoming v1.2 release, and has underpinned multiple scientific studies. In this work, we highlight the latest features of the API format, accompanying software tools, and provide an update on the implementation of OPTIMADE in contributing materials databases. We end by providing several use cases that demonstrate the utility of the OPTIMADE API in materials research that continue to drive its ongoing development.

Development of robust concrete mixes with a lower environmental impact is challenging due to natural variability in constituent materials and a multitude of possible combinations of mix proportions. Making reliable property predictions with machine learning can facilitate performance-based specification of concrete, reducing material inefficiencies and improving the sustainability of concrete construction. In this work, we develop a machine learning algorithm that can utilize intermediate target variables and their associated noise to predict the final target variable. We apply the methodology to specify a concrete mix that has high resistance to carbonation, and another concrete mix that has low environmental impact. Both mixes also fulfill targets on the strength, density, and cost. The specified mixes are experimentally validated against their predictions. Our generic methodology enables the exploitation of noise in machine learning, which has a broad range of applications in structural engineering and beyond., Comment: 21 pages (18 pages paper + 3 pages supplementary material)

We propose an element-agnostic set of descriptors to model superalloy properties with Gaussian process regression. Furthermore, we develop a correction method to deliver the best and most physical predictions for microchemistry in multi-phase alloys. The models' performance in predictions is confirmed for superalloy microchemistry, microstructure, and strength properties. When including new, unseen elements in the test data, the models still give good predictions; such extrapolations into new chemical-space would be impossible with component-based descriptors.

Noise and uncertainty are usually the enemy of machine learning, noise in training data leads to uncertainty and inaccuracy in the predictions. However, we develop a machine learning architecture that extracts crucial information out of the noise itself to improve the predictions. The phenomenology computes and then utilizes uncertainty in one target variable to predict a second target variable. We apply this formalism to PbZr$_{0.7}$Sn$_{0.3}$O$_{3}$ crystal, using the uncertainty in dielectric constant to extrapolate heat capacity, correctly predicting a phase transition that otherwise cannot be extrapolated. For the second example -- single-particle diffraction of droplets -- we utilize the particle count together with its uncertainty to extrapolate the ground truth diffraction amplitude, delivering better predictions than when we utilize only the particle count. Our generic formalism enables the exploitation of uncertainty in machine learning, which has a broad range of applications in the physical sciences and beyond., Comment: 13 pages, 10 figures. Appl Intell (2022)

Gaussian process regression machine learning with a physically-informed kernel is used to model the phase compositions of nickel-base superalloys. The model delivers good predictions for laboratory and commercial superalloys, with $R^2>0.8$ for all but two components of each of the $\gamma$ and $\gamma'$ phases, and $R^2=0.924$ ($\mathrm{RMSE}=0.063$) for the $\gamma'$ fraction. For four benchmark SX-series alloys the methodology predicts the $\gamma'$ phase composition with $\mathrm{RMSE}=0.006$ and the fraction with $\mathrm{RMSE}=0.020$, superior to the $0.007$ and $0.021$ respectively from CALPHAD. Furthermore, unlike CALPHAD Gaussian process regression quantifies the uncertainty in predictions, and can be retrained as new data becomes available.

Communal pairing in superconductors introduces variational freedom for Cooper pairs to share fermions. Temporal oscillations of the superconducting gap entropically drive communal pairing through the order by disorder phenomenology, stabilising a finite momentum space width of the superconducting gap that increases with interaction strength, creating a smooth evolution from the weakly interacting BCS state to the strongly interacting BEC state.

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification., Comment: 11 pages, 1 table

We perform molecular dynamics simulations to model density as a function of temperature for 74 alkanes with 5 to 10 carbon atoms and non-equilibrium molecular dynamics simulations in the NVT ensemble to model kinematic viscosity of 10 linear alkanes as a function of molecular weight, pressure, and temperature. To model density, we perform simulations in the NPT ensemble before applying correction factors to exploit the systematic error in the SciPCFF force field, and compare results to experimental values, obtaining an average absolute deviation of 3.4g/l at 25 $^{\circ}$ C and of 7.2g/l at 100 $^{\circ}$ C. We develop a sampling algorithm that automatically selects good shear rates at which to perform viscosity simulations in the NVT ensemble and use Carreau model with weighted least squares regression to extrapolate Newtonian viscosity. Viscosity simulations are performed at experimental densities and show an excellent agreement with experimental viscosities, with an average percent deviation of -1% and an average absolute percent deviation of 5%. Future plans to study and apply the sampling algorithm are outlined.

The quasi-harmonic model proposes that a crystal can be modeled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss' law shows that the ion-ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modeled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding, and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson's law. In the density tight-binding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearly-free electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ion-ion potential in all cases and we show that a first-order perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids., Comment: 10+12 pages, 6+7 figures

In the majority of molecular optimization tasks, predictive machine learning (ML) models are limited due to the unavailability and cost of generating big experimental datasets on the specific task. To circumvent this limitation, ML models are trained on big theoretical datasets or experimental indicators of molecular suitability that are either publicly available or inexpensive to acquire. These approaches produce a set of candidate molecules which have to be ranked using limited experimental data or expert knowledge. Under the assumption that structure is related to functionality, here we use a molecular fragment-based graphical autoencoder to generate unique structural fingerprints to efficiently search through the candidate set. We demonstrate that fragment-based graphical autoencoding reduces the error in predicting physical characteristics such as the solubility and partition coefficient in the small data regime compared to other extended circular fingerprints and string based approaches. We further demonstrate that this approach is capable of providing insight into real world molecular optimization problems, such as searching for stabilization additives in organic semiconductors by accurately predicting 92% of test molecules given 69 training examples. This task is a model example of black box molecular optimization as there is minimal theoretical and experimental knowledge to accurately predict the suitability of the additives.

We train artificial neural networks to predict the physical properties of linear, single branched, and double branched alkanes. These neural networks can be trained from fragmented data, which enables us to use physical property information as inputs and exploit property-property correlations to improve the quality of our predictions. We characterize every alkane uniquely using a set of five chemical descriptors. We establish correlations between branching and the boiling point, heat capacity, and vapor pressure as a function of temperature. We establish how the symmetry affects the melting point and identify erroneous data entries in the flash point of linear alkanes. Finally, we exploit the temperature and pressure dependence of shear viscosity and density in order to model the kinematic viscosity of linear alkanes. The accuracy of the neural network models compares favorably to the accuracy of several physico-chemical/thermodynamic methods., Comment: 12 pages, 17 figures, 6 tables

A spin-imbalanced Fermi gas with an attractive contact interaction forms a superconducting state whose underlying components are superpositions of Cooper pairs that share minority-spin fermions. This superconducting state includes correlations between all available fermions, making it energetically favorable to the Fulde--Ferrell--Larkin--Ovchinnikov superconducting state. The ratio of the number of up- and down-spin fermions in the instability is set by the ratio of the up- and down-spin density of states in momentum at the Fermi surfaces, to fully utilize the accessible fermions. We present analytical and complementary Diffusion Monte Carlo results for the state., Comment: 10 pages, 3 figures

Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of an arbitrary moment of a probability distribution with power-law heavy tails that exploits knowledge of the exponents of its asymptotic decay to bypass this issue entirely. Our method is applied to synthetic data and to energy and atomic force data from variational and diffusion quantum Monte Carlo calculations, whose distributions have known asymptotic forms [J. R. Trail, Phys. Rev. E 77, 016703 (2008); A. Badinski et al., J. Phys.: Condens. Matter 22 074202 (2010)]. We obtain convergent, accurate confidence intervals on the variance of the local energy of an electron gas and on the Hellmann-Feynman force on an atom in the all-electron carbon dimer. In each of these cases the uncertainty on our estimator is 45% and 60 times smaller, respectively, than the nominal (ill-defined) standard error., Comment: 17 pages, 17 figures; accepted in Phys. Rev. E

We develop a formalism to directly evaluate the matrix of force constants within a Quantum Monte Carlo calculation. We utilize the matrix of force constants to accurately relax the positions of atoms in molecules and determine their vibrational modes, using a combination of Variational and Diffusion Monte Carlo. The computed bond lengths differ by less than 0.007{\AA} from the experimental results for all four tested molecules. For hydrogen and hydrogen chloride, we obtain fundamental vibrational frequencies within 0.1% of experimental results and ~10 times more accurate than leading computational methods. For carbon dioxide and methane, the vibrational frequency obtained is on average within 1.1% of the experimental result, which is at least 3 times closer than results using Restricted Hartree-Fock and Density Functional Theory with a Perdew-Burke-Ernzerhof (PBE) functional and comparable or better than Density Functional Theory with a semi-empirical functional.

Entropic forces in classical many-body systems, e.g. colloidal suspensions, can lead to the formation of new phases. Quantum fluctuations can have similar effects: spin fluctuations drive the superfluidity of Helium-3 and a similar mechanism operating in metals can give rise to superconductivity. It is conventional to discuss the latter in terms of the forces induced by the quantum fluctuations. However, focusing directly upon the free energy provides a useful alternative perspective in the classical case and can also be applied to study quantum fluctuations. Villain first developed this approach for insulating magnets and coined the term order-by-disorder to describe the observed effect. We discuss the application of this idea to metallic systems, recent progress made in doing so, and the broader prospects for the future., Comment: Submitted to Annual Review of Condensed Matter Physics. 14 pages 6 figures

We develop ultratransferable pseudopotentials for the contact interaction that are 100 times more accurate than contemporary approximations. The pseudopotential offers scattering properties very similar to the contact potential, has a smooth profile to accelerate numerics by a factor of up to 4,000, and, for positive scattering lengths, does not support an unwanted bound state. We demonstrate these advantages in a Diffusion Monte Carlo study of fermions with repulsive interactions, delivering the first numerical evidence for the formation of a p-wave superconducting state.