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The design of functional materials with desired properties is essential in driving technological advances in areas such as energy storage, catalysis and carbon capture 1 , 2 – 3 . Generative models accelerate materials design by directly generating new materials given desired property constraints, but current methods have a low success rate in proposing stable crystals or can satisfy only a limited set of property constraints 4 , 5 , 6 , 7 , 8 , 9 , 10 – 11 . Here we present MatterGen, a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints. Compared with previous generative models 4 , 12 , structures produced by MatterGen are more than twice as likely to be new and stable, and more than ten times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, new materials with desired chemistry, symmetry and mechanical, electronic and magnetic properties. As a proof of concept, we synthesize one of the generated structures and measure its property value to be within 20% of our target. We believe that the quality of generated materials and the breadth of abilities of MatterGen represent an important advancement towards creating a foundational generative model for materials design. MatterGen is a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints.

The simulation and analysis of the thermal stability of nanoparticles, a stepping stone towards their application in technological devices, require fast and accurate force fields, in conjunction with effective characterisation methods. In this work, we develop efficient, transferable, and interpretable machine learning force fields for gold nanoparticles based on data gathered from Density Functional Theory calculations. We use them to investigate the thermodynamic stability of gold nanoparticles of different sizes (1 to 6 nm), containing up to 6266 atoms, concerning a solid-liquid phase change through molecular dynamics simulations. We predict nanoparticle melting temperatures in good agreement with available experimental data. Furthermore, we characterize the solid-liquid phase change mechanism employing an unsupervised learning scheme to categorize local atomic environments. We thus provide a data-driven definition of liquid atomic arrangements in the inner and surface regions of a nanoparticle and employ it to show that melting initiates at the outer layers. Efficient theoretical methods for the structural analysis of nanoparticles are very much needed. Here the authors demonstrate the use of machine-learning force fields and of a data-driven approach to study the thermodynamical stability and elucidate the melting process of gold nanoparticles.

Machine learning algorithms have recently emerged as a tool to generate force fields which display accuracies approaching the ones of the ab-initio calculations they are trained on, but are much faster to compute. The enhanced computational speed of machine learning force fields results key for modelling metallic nanoparticles, as their fluxionality and multi-funneled energy landscape needs to be sampled over long time scales. In this review, we first formally introduce the most commonly used machine learning algorithms for force field generation, briefly outlining their structure and properties. We then address the core issue of training database selection, reporting methodologies both already used and yet unused in literature. We finally report and discuss the recent literature regarding machine learning force fields to sample the energy landscape and study the catalytic activity of metallic nanoparticles.

Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using subsets of these features. Finding a small set of features that still retains sufficient information about the dataset is important for the successful application of many statistical learning approaches. We introduce a statistical test that can assess the relative information retained when using 2 different distance measures, and determine if they are equivalent, independent, or if one is more informative than the other. This ranking can in turn be used to identify the most informative distance measure and, therefore, the most informative set of features, out of a pool of candidates. To illustrate the general applicability of our approach, we show that it reproduces the known importance ranking of policy variables for Covid-19 control, and also identifies compact yet informative descriptors for atomic structures. We further provide initial evidence that the information asymmetry measured by the proposed test can be used to infer relationships of causality between the features of a dataset. The method is general and should be applicable to many branches of science.

The recent years have seen a surge in the development of machine learning algorithms in different areas of scientific research. In the field of simulation of materials, the development of machine learning force fields to carry out fast and accurate molecular dynamics simulations has been attracting a lot of interest ever since the early manuscripts of Blank et al. in 1995, Brown et al. in 1996, and the pioneering work of Behler and Parrinello in 2007. Machine learning force fields are trained using reference data coming from expensive ab initio simulations and try to approximate these accurate methods without recurring to any ad hoc fitting procedure in a computationally efficient way. In this thesis, we present the work done on the development of algorithms that employ Gaussian process regression to build machine learning force fields. We specifically design Gaussian process force fields that use explicitly 2-body, 3-body, and simplified many-body descriptors of local atomic environments. Furthermore, we develop an algorithm to map such Gaussian process force fields into nonparametric classical force fields. This rather general “mapping” procedure removes the inefficient computational scaling of Gaussian process regression methods and yields, without meaningful accuracy losses, force fields that are as fast as classical parametric force fields. All the algorithms and numerical procedures discussed in this thesis are available as a Python package, named “MFF”, which I have coauthored. This package is freely available at https://github.com/kcl-tscm/mff, and fully documented. To benchmark the speed and accuracy of the MFF package, we test it on bulk metals (Fe, Ni) and semiconductors (C, Si). We also address the problem of developing machine learning force fields for metallic nanoparticles such as Ni, Au and AgAu. Nanoparticles display very complex energetic landscapes, and accurate force fields that are not fitted on bulk properties are highly desirable to predict structural transitions and phase changes. We build force fields for a set of five isomers of Ni19, and carry out classical molecular dynamics simulations for a total of ∼ 200 ns, a time scale not reachable via ab initio methods, but indeed easily accessible using our mapped machine learning force fields. Subsequently, we discuss the development of machine learning force fields that are accurate for nanoparticles with varying numbers of atoms and analyse small Ni nanoparticles containing 13 to 20 atoms, and larger Au nanoparticles containing 147, 309 and 561 atoms. For the smaller Ni nanoparticles, machine learning force fields are not transferable between particle sizes, reinforcing the belief that “every atom counts” in small nanoparticles. For larger Au nanoparticles, force fields trained on Au147 data well predict forces in the two bigger Au nanoparticles; this result paves the way towards the development of machine learning force fields which are accurate for nanoparticles that contain too many atoms to be effectively simulated using quantum methods.

Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using subsets of these features. Using the fewest features but still retaining sufficient information about the system is crucial in many statistical learning approaches, particularly when data are sparse. We introduce a statistical test that can assess the relative information retained when using two different distance measures, and determine if they are equivalent, independent, or if one is more informative than the other. This in turn allows finding the most informative distance measure out of a pool of candidates. The approach is applied to find the most relevant policy variables for controlling the Covid-19 epidemic and to find compact yet informative representations of atomic structures, but its potential applications are wide ranging in many branches of science.

We show that, contrary to popular assumptions, predictions from machine learning potentials built upon high-dimensional atom-density representations almost exclusively occur in regions of the representation space which lie outside the convex hull defined by the training set points. We then propose a perspective to rationalize the domain of robust extrapolation and accurate prediction of atomistic machine learning potentials in terms of the probability density induced by training points in the representation space

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors.

The simulation and analysis of the thermal stability of nanoparticles, a stepping stone towards their application in technological devices, require fast and accurate force fields, in conjunction with effective characterisation methods. In this work, we develop efficient, transferable, and interpretable machine learning force fields for gold nanoparticles based on data gathered from Density Functional Theory calculations. We use them to investigate the thermodynamic stability of gold nanoparticles of different sizes (1 to 6 nm), containing up to 6266 atoms, concerning a solid-liquid phase change through molecular dynamics simulations. We predict nanoparticle melting temperatures in good agreement with available experimental data. Furthermore, we characterize the solid-liquid phase change mechanism employing an unsupervised learning scheme to categorize local atomic environments. We thus provide a data-driven definition of liquid atomic arrangements in the inner and surface regions of a nanoparticle and employ it to show that melting initiates at the outer layers.

DADApy is a python software package for analysing and characterising high-dimensional data manifolds. It provides methods for estimating the intrinsic dimension and the probability density, for performing density-based clustering and for comparing different distance metrics. We review the main functionalities of the package and exemplify its usage in toy cases and in a real-world application. DADApy is freely available under the open-source Apache 2.0 license.