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Potentiels répulsifs transférables pour la méthode Density Functional based Tight-Binding : approche novatrice par apprentissage automatique

Abstract : During the last decade, atomistic simulation landscape has seen the rise of numeroususes of machine-learning tools. As most teams obviously focus on rather varied applications, all of them still push in a similar direction : reshaping the tradeoff between accuracy and compuational time. However, for purely numerical tools, the gain of perrformance is often linked to a loss of information (eg. electronic structure or a heavy reliance on purely mathematical, with few physical ground. Semi-empirical methods are much older, such as the Density Functional based Tight-Binding method (DFTB) which appeared at the end of the previous century. Yet, they share the very same motivation : to relieve first principle methods, such as Density Functional Theory (DFT) , from their heavy quantum mechanics calculation without the characteristic accuracy drop implied. This is achieved by keeping a quantum formalism - hence still accessing electronic propertie - and performing highly physical approximations in order to precompute key parameters. This process allows to reduce the computation time and the accuracy loss is marginal. Within the DFTB formalism, the main approximation is the computation of the repulsive potential as a simple sum of pair interactions depending on the interatomic distance. This representation is limited by its simple functional form, while also being the approximation with the weakest physical ground. This thesis redefine this term as a many-body interaction, and to do so we use machine-learning tools. From the concept of atomic environment, we opt for a description adpated to the symmetries of the system (Atom-Centered Symmetry functions) and we use high dimensional neural networks to predict the repulsive energy. We apply this methodology to the case of pure Silicon, by aiming to build a global purpose repulsive potential for this element. We first build a set of reference data from first principle computations, including monocrystalline polymorphs, disordered phaes and nano-clulsters. We then train neural-network with a specific focus on short interatomic distances, and obtain a repulsive potential that is plugged within the DFTB+ code. The evaluation of our tool's performance is done for each of those systems : relative stability, radial and angular distribution functions, vibrational densities of states, binding/formation energies, compacity measure. In each case, we compare the results to the DFT reference, t pair-repulsive potentials and to two pure ML-approaches (ie. aiming to directly reproduce DFT). The overall performance are satisfying : for condensed systems, our tool stands as a sensitive improve over pair-repulsive potentials. In this case, comparison with pure ML tools lets us state that our choice to only focus on a sub-part of the total energy limits the overall performance by hampering the flexibility of our tools ; this also comes with a more robust behaviour. For nano-clusters, all ML-approaches are rather mediocre ; this can be partially explained by delocalized interactions in non-periodic systems, as well as by the strong importance of surface effects. The functionally more robust pair-repulsive potentials are more reliable, hence more uesful.
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Submitted on : Friday, June 24, 2022 - 4:09:11 PM
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  • HAL Id : tel-03704165, version 1



Dylan Bissuel. Potentiels répulsifs transférables pour la méthode Density Functional based Tight-Binding : approche novatrice par apprentissage automatique. Physique [physics]. Université de Lyon, 2021. Français. ⟨NNT : 2021LYSE1276⟩. ⟨tel-03704165⟩



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