Description du sujet de thèse

The aim is to study the evolution of atoms during the crystallization of a metal. Indeed, in the liquid state, a system is composed of atoms without structure, while in the crystal state, a perfect structure emerges in the order of the atoms. The illustration shows the case of Tantalum, with a face-centered cubic lattice structure for the red crystal and complete disorder for the blue liquid. During the crystallization process, the atoms align, but the way they organize is not yet well understood.
In this thesis, we propose to develop a machine learning method that will build groups (clusters) on the dynamic model. Initially, we observe the liquid, so we expect a very heterogeneous cluster. At the end of the process, we observe the crystal, so we expect a very homogeneous cluster. But during the process, we hope to see the emergence of different clusters, which will show the geometry of crystallization and the competition between structures.
This study was initiated at fixed times as part of a previous thesis [1]. In this project, we wish to extend this work by including dynamics.
From a modeling point of view, an atom is considered with its neighbors to have a vision of the local structure. Usually, a local structure consists of the atom and its nearest neighbors, but the works of Sébastien Becker's thesis [1] showed richer information in the second neighborhood. We can then consider the trajectory of these structures as time series and seek to group these structures, these groups evolving over time.
Unsupervised learning, or group construction, is a classic problem in machine learning, and many methods have been developed [2] (hierarchical classification, neighborhood, mixture models, ...). The temporal aspect is fundamental in this project: the evolution of groups over time is the main object of study to conclude in materials science. One idea is to segment time into homogeneous intervals, within which fixed clustering can be done [3]. The segmentation hypothesis is nonetheless strong on this data, which evolves rather continuously. We can then be inspired by the temporal method developed in [4], which penalizes groupings in order to have groups consistent with time. However, here, we want the groups to be constructed on networks (each individual is a network), so the encoding of this data needs work.
The idea is to develop a parametric model, which can be analyzed a posteriori on crystallization data.

Contexte de travail

This thesis will be conducted within the framework of the international ANR project SOLIMAT with Germany and co-directed between the SIMAP and LIG laboratories. Regular trips to Germany will be anticipated for the smooth progression of the project.

Contraintes et risques

no constraints