Phd in THEORETICAL AND APPLIED MECHANICS

Thesis title: Deep learning collective variables for structural transitions in metal nanoclusters

The objective of my thesis is the development of machine learning tools for the description and biasing of molecular simulations and the study of rare events. Neural networks were leveraged in order to devise collective variables able to properly describe the complex structural landscapes of atomic systems. I subsequently demonstrated how, using these deep coordinates, it is possible to navigate the system's structural landscape and to compute of the thermodynamics of the different structural metastable states via established techniques such as umbrella sampling and histogram reweighting. The case study on which these techniques were developed and tested is that of structural transitions in metal nanoclusters of some hundreds of atoms. These systems appeared to be the optimal testing ground for the development of such methods, owing to their rich structural complexity combined with a limited computational cost due to their small atomic size. The first step towards the construction of a suitable neural network consisted in the search for a proper descriptor able to finely distinguish between the different structural features of metal nanoclusters. This descriptor was found in the radial distribution function for the whole cluster, after which the information contained in this high dimensional description was distilled via a dimensionality reduction which allowed me to obtain a convenient and insightful representation of the system's structural landscape. In order to perform the dimensionality reduction step, a specific neural networks architecture was adopted, known as \emph{convolutional autoencoder}, which is particularly suited for dimensionality reduction tasks of sequences. Dimensionality reduction was performed on large amount of atomistic data, which had been previously generated via dedicated parallel tempering molecular simulations. The resulting low dimensional space proved to be well versed at characterizing and discriminating the different metastable states of the system exploiting clustering techniques. Closely related descriptors could also be used as collective variables in enhanced sampling simulations that allowed to quantitatively characterize the thermodynamics of transitions between different nanocluster structures.