Characterising the geometry of image space of nanostructures for inferential analysis of dewetting processes and computational models

The self-assembly of nanostructures has been of growing interest in materials science, with particular advancements in the development of computational models that describe this self-assembly. So far, however, the utility of these models have been limited by the absence of methods to relate real experimental data with numerical simulations or the experimental and simulation conditions that generate them. We have 2625 real atomic force microscope (AFM) gray-scale images of nanoparticle depositions produced through dewetting experiments and two computational models that simulate these experiments; a kinetic Monte Carlo (KMC) model and a dynamical density functional theory (DDFT) model. In this thesis, we first propose an automated neural network segmentation method to minimise noise in the real images and allow meaningful comparison with simulated images. We then characterise the geometry of the image space through defining a map to a feature space. The statistics we use as coordinates in this space are novel modifications of the Minkowski functionals. This space provides evidence of the possibility of meaningful comparison between real and simulated images. The modified Minkowski functionals are then used to make quantitative descriptions of the behaviour of the computational models. Finally, we are able to fit accurate predictive models of the types of structures we expect to see from given simulation conditions. We discuss the promise this shows for successfully carrying out the inverse problem but note that the modified Minkowski functionals are insufficient for this task by themselves and consider Riemannian geometry as a more suitable approach.