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Personne# Chiheb Ben Mahmoud

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Chiheb Ben Mahmoud, Michele Ceriotti, Nataliya Lopanitsyna

Atomistic simulations provide insights into structure-property relations on an atomic size and length scale, that are complementary to the macroscopic observables that can be obtained from experiments. Quantitative predictions, however, are usually hindered by the need to strike a balance between the accuracy of the calculation of the interatomic potential and the modeling of realistic thermodynamic conditions. Machine-learning techniques make it possible to efficiently approximate the outcome of accurate electronic-structure calculations, that can therefore be combined with extensive thermodynamic sampling. We take elemental nickel as a prototypical material, whose alloys have applications from cryogenic temperatures up to close to their melting point, and use it to demonstrate how a combination of machine-learning models of electronic properties and statistical sampling methods makes it possible to compute accurate finite-temperature properties at an affordable cost. We demonstrate the calculation of a broad array of bulk, interfacial, and defect properties over a temperature range from 100 to 2500 K, modeling also, when needed, the impact of nuclear quantum fluctuations and electronic excitations. The framework we demonstrate here can be easily generalized to more complex alloys and different classes of materials.

2021Chiheb Ben Mahmoud, Michele Ceriotti, Federico Grasselli

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 Letter 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 modeling by removing the barrier between physics and data-driven methodologies.

The electronic density of states (DOS) quantifies the distribution of the energy levels that can be occupied by electrons in a quasiparticle picture and is central to modern electronic structure theory. It also underpins the computation and interpretation of experimentally observable material properties such as optical absorption, electrical conductivity, and heat capacity. It can be accurately computed through expensive first-principle calculations, limiting the size of the problems that can be simulated easily to a few thousand atoms. Machine-learning (ML) techniques are a promising alternative to these calculations, as they were successfully applied to study many atomic-scale problems by generalising information from small configurations to large and complex structures. However, most efforts focused on learning the ground-state Born-Oppenheimer energies and the atomic forces, which are scalar quantities, unlike the DOS, which is a multivariate function of the energy. In this thesis, we discuss the inherent challenges in constructing an ML framework that predicts the DOS as a combination of local contributions that depend, in turn, on the geometric configuration of neighbours around each atom. We compare different approaches to represent the DOS as a learning target and the accuracy of predicting quantities such as the Fermi level, the electron density at the Fermi level, or the band energy, either directly or as a side product of the evaluation of the DOS. As a first benchmark, we evaluate our model on a challenging case study that includes configurations of silicon spanning a broad set of thermodynamic conditions, ranging from bulk structures to clusters and from semiconducting to metallic behaviour. Then, we leverage the atom-centredness of the model to compute the DOS of large amorphous silicon samples, for which it would be prohibitively expensive to compute the DOS by direct electronic structure calculations. Besides the size transferability, we show that this decomposition of the DOS can extract physical insights into the connections between structural and electronic features to describe their transitions in disordered phases.Finally, we explore two approaches to using the DOS in integrated ML frameworks to model the properties of materials, where the DOS is used to incorporate the effect of thermal excitations of electrons. We propose to combine simulations from well-established ML interatomic potentials with band energy calculations extracted from DOS predictions on the already-produced trajectories. This procedure successfully describes the heat capacity of molten nickel and is in agreement with the experiments. However, we show that this method is only valid when the dynamics of the ions are, to a large extent, not affected by the electronic excitations, and it would fail in conditions with higher temperatures, such as those found in astrophysical settings. Therefore, we introduce an integrated ML framework that includes these thermal effects in constructing the interatomic potential. The novelty of this method is that the electronic temperature is an external parameter of the simulation because one only needs access to ground-state energies, forces and DOS. We successfully apply our model to study metallic hydrogen in the conditions of a young Jupiter core. We reconstruct its equation of state and its heat capacity and find that they are compatible with their first-principle-derived counterparts.