arXiv subjects

Michele Ceriotti

Publications and source records attributed to Michele Ceriotti.

At least 73 records · Page 4Linked to original sources

arXiv2023

Probing the unfolded configurations of a $β$-hairpin using sketch-map

This work examines the conformational ensemble involved in $β$-hairpin folding by means of advanced molecular dynamics simulations and dimensionality reduction. A fully atomistic description of the protein and the surrounding solvent molecules is used and this complex energy landscape is sampled by means of parallel tempering metadynamics simulations. The ensemble of configurations explored is analysed using the recently proposed sketch-map algorithm. Further simulations allow us to probe how mutations affect the structures adopted by this protein. We find that many of the configurations adopted by a mutant are the same as those adopted by the wild type protein. Furthermore, certain mutations destabilize secondary structure containing configurations by preventing the formation of hydrogen bonds or by promoting the formation of new intramolecular contacts. Our analysis demonstrates that machine-learning techniques can be used to study the energy landscapes of complex molecules and that the visualizations that are generated in this way provide a natural basis for examining how the stabilities of particular configurations of the molecule are affected by factors such as temperature or structural mutations.

physics.chem-ph↗

arXiv2023

A smooth basis for atomistic machine learning

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighbourhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to expand the angular dependence of this density, but there is as yet no clear rationale to choose one radial basis over another. Here we investigate the basis that results from the solution of the Laplacian eigenvalue problem within a sphere around the atom of interest. We show that this generates the smoothest possible basis of a given size within the sphere, and that a tensor product of Laplacian eigenstates also provides the smoothest possible basis for expanding any higher-order correlation of the atomic density within the appropriate hypersphere. We consider several unsupervised metrics of the quality of a basis for a given dataset, and show that the Laplacian eigenstate basis has a performance that is much better than some widely used basis sets and is competitive with data-driven bases that numerically optimize each metric. In supervised machine learning tests, we find that the optimal function smoothness of the Laplacian eigenstates leads to comparable or better performance than can be obtained from a data-driven basis of a similar size that has been optimized to describe the atom-density correlation for the specific dataset. We conclude that the smoothness of the basis functions is a key and hitherto largely overlooked aspect of successful atomic density representations.

physics.chem-ph↗

arXiv2023

Fast evaluation of spherical harmonics with sphericart

Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from geology and atmospheric sciences to signal processing and computer graphics. More recently, they have become a key component of rotationally equivariant models in geometric machine learning, including applications to atomic-scale modeling of molecules and materials. We present an elegant and efficient algorithm for the evaluation of the real-valued spherical harmonics. Our construction features many of the desirable properties of existing schemes and allows to compute Cartesian derivatives in a numerically stable and computationally efficient manner. To facilitate usage, we implement this algorithm in sphericart, a fast C++ library which also provides C bindings, a Python API, and a PyTorch implementation that includes a GPU kernel.

physics.chem-ph↗

arXiv2023

Modeling high-entropy transition-metal alloys with alchemical compression

Alloys composed of several elements in roughly equimolar composition, often referred to as high-entropy alloys, have long been of interest for their thermodynamics and peculiar mechanical properties, and more recently for their potential application in catalysis. They are a considerable challenge to traditional atomistic modeling, and also to data-driven potentials that for the most part have memory footprint, computational effort and data requirements which scale poorly with the number of elements included. We apply a recently proposed scheme to compress chemical information in a lower-dimensional space, which reduces dramatically the cost of the model with negligible loss of accuracy, to build a potential that can describe 25 d-block transition metals. The model shows semi-quantitative accuracy for prototypical alloys, and is remarkably stable when extrapolating to structures outside its training set. We use this framework to study element segregation in a computational experiment that simulates an equimolar alloy of all 25 elements, mimicking the seminal experiments by Cantor et al., and use our observations on the short-range order relations between the elements to define a data-driven set of Hume-Rothery rules that can serve as guidance for alloy design. We conclude with a study of three prototypical alloys, CoCrFeMnNi, CoCrFeMoNi and IrPdPtRhRu, determining their stability and the short-range order behavior of their constituents.

cond-mat.mtrl-sci↗

arXiv2023

Wigner kernels: body-ordered equivariant machine learning without a basis

Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different approaches that have been pursued, the description of local atomic environments in terms of their neighbor densities has been used widely and very succesfully. We propose a novel density-based method which involves computing ``Wigner kernels''. These are fully equivariant and body-ordered kernels that can be computed iteratively with a cost that is independent of the radial-chemical basis and grows only linearly with the maximum body-order considered. This is in marked contrast to feature-space models, which comprise an exponentially-growing number of terms with increasing order of correlations. We present several examples of the accuracy of models based on Wigner kernels in chemical applications, for both scalar and tensorial targets, reaching state-of-the-art accuracy on the popular QM9 benchmark dataset, and we discuss the broader relevance of these ideas to equivariant geometric machine-learning.

physics.chem-ph↗

arXiv2022

A data-driven interpretation of the stability of molecular crystals

Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of different interactions enables the design of molecular crystals and fine-tuning their stabilities. While this is usually performed based on the empirical observation of the most commonly encountered motifs in known crystal structures, we propose to apply a combination of supervised and unsupervised machine-learning techniques to automate the construction of an extensive library of molecular building blocks. We introduce a structural descriptor tailored to the prediction of the binding (lattice) energy and apply it to a curated dataset of organic crystals and exploit its atom-centered nature to obtain a data-driven assessment of the contribution of different chemical groups to the lattice energy of the crystal. We then interpret this library using a low-dimensional representation of the structure-energy landscape and discuss selected examples of the insights into crystal engineering that can be extracted from this analysis, providing a complete database to guide the design of molecular materials.

physics.chem-ph↗

arXiv2022

Incompleteness of graph neural networks for points clouds in three dimensions

Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e., there exist graphs that are distinct but appear identical when seen through the lens of the GNN. More complicated schemes have thus been designed to increase their resolving power. Applications to molecules (and more generally, point clouds), however, add a geometric dimension to the problem. The most straightforward and prevalent approach to construct graph representation for molecules regards atoms as vertices in a graph and draws a bond between each pair of atoms within a chosen cutoff. Bonds can be decorated with the distance between atoms, and the resulting "distance graph NNs" (dGNN) have empirically demonstrated excellent resolving power and are widely used in chemical ML, with all known indistinguishable configurations being resolved in the fully-connected limit, which is equivalent to infinite or sufficiently large cutoff. Here we present a counterexample that proves that dGNNs are not complete even for the restricted case of fully-connected graphs induced by 3D atom clouds. We construct pairs of distinct point clouds whose associated graphs are, for any cutoff radius, equivalent based on a first-order Weisfeiler-Lehman test. This class of degenerate structures includes chemically-plausible configurations, both for isolated structures and for infinite structures that are periodic in 1, 2, and 3 dimensions. The existence of indistinguishable configurations sets an ultimate limit to the expressive power of some of the well-established GNN architectures for atomistic machine learning. Models that explicitly use angular or directional information in the description of atomic environments can resolve this class of degeneracies.

stat.ML↗

arXiv2022

Predicting hot-electron free energies from ground-state data

Machine-learning potentials are usually trained on the ground-state, Born-Oppenheimer energy surface, which depends exclusively on the atomic positions and not on the simulation temperature. This disregards the effect of thermally-excited electrons, that is important in metals, and essential to the description of warm dense matter. An accurate physical description of these effects requires that the nuclei move on a temperature-dependent electronic free energy. We propose a method to obtain machine-learning predictions of this free energy at an arbitrary electron temperature using exclusively training data from ground-state calculations, avoiding the need to train temperature-dependent potentials, and benchmark it on metallic liquid hydrogen at the conditions of the core of gas giants and brown dwarfs. This work demonstrates the advantages of hybrid schemes that use physical consideration to combine machine-learning predictions, providing a blueprint for the development of similar approaches that extend the reach of atomistic modelling by removing the barrier between physics and data-driven methodologies.

cond-mat.mtrl-sci↗

arXiv2022

Thermodynamics and dielectric response of $\text{BaTiO}_3$ by data-driven modeling

Modeling ferroelectric materials from first principles is one of the successes of density-functional theory, and the driver of much development effort, requiring an accurate description of the electronic processes and the thermodynamic equilibrium that drive the spontaneous symmetry breaking and the emergence of macroscopic polarization. We demonstrate the development and application of an integrated machine learning model that describes on the same footing structural, energetic and functional properties of barium titanate ($\text{BaTiO}_3$), a prototypical ferroelectric. The model uses ab initio calculations as reference and achieves accurate yet inexpensive predictions of energy and polarization on time and length scales that are not accessible to direct ab initio modeling. These predictions allow us to assess the microscopic mechanism of the ferroelectric transition. The presence of an order-disorder transition for the Ti off-centered states is the main driver of the ferroelectric transition, even though the coupling between symmetry breaking and cell distortions determines the presence of intermediate, partly-ordered phases. Moreover, we thoroughly probe the static and dynamical behavior of $\text{BaTiO}_3$ across its phase diagram, without the need to introduce a coarse-grained description of the ferroelectric transition. Finally, we apply the polarization model to calculate dielectric response properties of the material in a fully ab initio manner, again reproducing the correct qualitative experimental behaviour.

cond-mat.mtrl-sci↗

arXiv2022

Beyond potentials: integrated machine-learning models for materials

Over the past decade inter-atomic potentials based on machine-learning (ML) techniques have become an indispensable tool in the atomic-scale modeling of materials. Trained on energies and forces obtained from electronic-structure calculations, they inherit their predictive accuracy, and extend greatly the length and time scales that are accessible to explicit atomistic simulations. Inexpensive predictions of the energetics of individual configurations have facilitated greatly the calculation of the thermodynamics of materials, including finite-temperature effects and disorder. More recently, machine-learning models have been closing the gap with first-principles calculations in another area: the prediction of arbitrarily complicated functional properties, from vibrational and optical spectroscopies to electronic excitations. The implementation of integrated machine-learning models, that combine energetic and functional predictions with statistical and dynamical sampling of atomic-scale properties is bringing the promise of predictive, uncompromising simulations of existing and novel materials closer to its full realisation.

cond-mat.mtrl-sci↗

arXiv2022

Electronic-structure properties from atom-centered predictions of the electron density

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multi-centered atomic basis analogous to that routinely used in density fitting approximations. However, the non-orthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex datasets, obtaining extremely accurate predictions. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark dataset, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.

physics.chem-ph↗

arXiv2022

Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four body interactions"

The "quasi-constant" SOAP and ACSF fingerprint manifolds recently discovered by Parsaeifard and Goedecker are a direct consequence of the presence of degenerate pairs of configurations, a known shortcoming of all low-body-order atom-density correlation representations of molecular structures. Contrary to the configurations that are rigorously singular -- that we demonstrate can only occur in finite, discrete sets -- the continuous "quasi-constant" manifolds exhibit low, but non-zero, sensitivity to atomic displacements. Thus, it is possible to build interpolative machine-learning models of high-order interactions along the manifold, even though the numerical instabilities associated with proximity to the exact singularities affect the accuracy and transferability of such models, to an extent that depends on numerical details of the implementation.

physics.chem-ph↗

arXiv2022

Unified theory of atom-centered representations and message-passing machine-learning schemes

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, that are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), that are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes, that gather information on the relationship between neighboring atoms using "message-passing" ideas, cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and provides a coherent foundation to systematize our understanding of both atom-centered and message-passing, invariant and equivariant machine-learning schemes.

stat.ML↗

arXiv2022

Modeling the Ga/As binary system across temperaturesand compositions from first principles

Materials composed of elements from the third and fifth columns of the periodic table display a very rich behavior, with the phase diagram usually containing a metallic liquid phase and a polar semiconducting solid. As a consequence, it is very hard to achieve transferable empirical models of interactions between the atoms that can reliably predict their behavior across the temperature and composition range that is relevant to the study of the synthesis and properties of III/V nanostructures and devices. We present a machine-learning potential trained on density functional theory reference data that provides a general-purpose model for the Ga$_x$As$_{1-x}$ system. We provide a series of stringent tests that showcase the accuracy of the potential, and its applicability across the whole binary phase space, computing with ab initio accuracy a large number of finite-temperature properties as well as the location of phase boundaries. We also show how a committe model can be used to reliably determine the uncertainty induced by the limitations of the ML model on its predictions, to identify regions of phase space that are predicted with insufficient accuracy, and to iteratively refine the training set to achieve consistent, reliable modeling.

cond-mat.mtrl-sci↗

arXiv2022

Optimal radial basis for density-based atomic representations

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations can be seen as an expansion of the symmetrized correlations of the atom density, and differ mainly by the choice of basis. Considerable effort has been dedicated to the optimization of the basis set, typically driven by heuristic considerations on the behavior of the regression target. Here we take a different, unsupervised viewpoint, aiming to determine the basis that encodes in the most compact way possible the structural information that is relevant for the dataset at hand. For each training dataset and number of basis functions, one can determine a unique basis that is optimal in this sense, and can be computed at no additional cost with respect to the primitive basis by approximating it with splines. We demonstrate that this construction yields representations that are accurate and computationally efficient, particularly when constructing representations that correspond to high-body order correlations. We present examples that involve both molecular and condensed-phase machine-learning models.

stat.ML↗

arXiv2022

The importance of nuclear quantum effects for NMR crystallography

The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for $^1$H, $^{13}$C, and $^{15}$N shieldings in polymorphs of three paradigmatic molecular crystals -- benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typical errors of shielding predictions for static nuclei with respect to experiments, and their inclusion to improve the agreement with measurements, translating to more reliable assignment of the NMR spectra to the correct candidate structure. The use of integrated machine-learning models, trained on first-principles energies and shieldings, renders rigorous sampling of nuclear fluctuations affordable, setting a new standard for the calculations underlying NMR structure determinations.

physics.chem-ph↗

arXiv2021

Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each structure. In most cases, the models rely on a description of atom-centered environments, and are suitable to learn atomic properties, or global observables that can be decomposed into atomic contributions. Many quantities that are relevant for quantum mechanical calculations, however -- most notably the single-particle Hamiltonian matrix when written in an atomic-orbital basis -- are not associated with a single center, but with two (or more) atoms in the structure. We discuss a family of structural descriptors that generalize the very successful atom-centered density correlation features to the N-centers case, and show in particular how this construction can be applied to efficiently learn the matrix elements of the (effective) single-particle Hamiltonian written in an atom-centered orbital basis. These N-centers features are fully equivariant -- not only in terms of translations and rotations, but also in terms of permutations of the indices associated with the atoms -- and are suitable to construct symmetry-adapted machine-learning models of new classes of properties of molecules and materials.

physics.chem-ph↗

arXiv2021

Learning electron densities in the condensed phase

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centred auxiliary basis, which enables an accurate expansion of the all-electron density in a form suitable for learning isolated and periodic systems alike. We show that using this formulation the electron densities of metals, semiconductors and molecular crystals can all be accurately predicted using symmetry-adapted Gaussian process regression models, properly adjusted for the non-orthogonal nature of the basis. These predicted densities enable the efficient calculation of electronic properties which present errors on the order of tens of meV/atom when compared to ab initio density-functional calculations. We demonstrate the key power of this approach by using a model trained on ice unit cells containing only 4 water molecules to predict the electron densities of cells containing up to 512 molecules, and see no increase in the magnitude of the errors of derived electronic properties when increasing the system size. Indeed, we find that these extrapolated derived energies are more accurate than those predicted using a direct machine-learning model. Finally, on heterogeneous datasets SALTED can predict electron densities with errors below 4%.

physics.chem-ph↗