Parameter identification by eigenfeature analysis: application to 2D Kuramoto-Sivashinsky surface models

We have developed a system that makes it possible to derive parameters of a Kuramoto-Sivashinsky (KS) model from a single given two-dimensional profile of surface structures, such as those produced by ion and plasma irradiation. The numerical method is inspired by well-known approaches to facial recognition. Starting from a scaled version of a KS Model to describe surface erosion, a training set of surface profiles is created. Each profile is assigned an appropriate feature in Fourier space and a Singular Value Decomposition is used to determine an orthogonal set of eigenfeatures that allow each profile to be assigned a point in the space of this basis and to determine the distances between them. It turns out that the profiles belonging to different model parameters are clearly separated from each other in this feature space, which enables very good identification. We explain the basic relationships using a synthetic data set and discuss the possibilities for applications to experimental results.