Vision transformer based parameter estimation for 2D Kuramoto–Sivashinsky models using physics informed features

Abstract Bombarding a surface with ions can cause the development of surface nanostructures. There exists a continuum model to describe the evolution of such surfaces with a partial differential equation. This equation is of the Kuramoto–Sivashinsky (KS) type, which depends on several parameters explaining the various physical processes that participate in the evolution of the surface. Using a normalized version of the KS equation, we have created a dataset of KS surfaces for a wide range of parameter sets. We have developed and trained a neural network model, based on the vision transformer architecture, to predict the KS parameters for a given surface. The inputs for this model are the surface height function h ( x , y ) , the local surface inclination angle δ ( x , y ) and the Laplacian of the height function Δ h ( x , y ) , this reduces the mean squared validation error in training by an order of magnitude, when compared to only using h ( x , y ) . The model is able to predict the KS parameters for the test surfaces with a mean average error of ∼ 1.48 % of the used parameter range, showing good interpolation, and even some extrapolation capability. Furthermore, a low dimensional embedding for the surfaces was found, containing information on the different parameter regimes. Our model shows that it is possible to learn the complex connection between the parameters and results of a chaotic nonlinear process, with acceptable computational expense. This work aims to explore the path to AI models that help researchers working on ion beam sputtering experiments to quickly find theoretical models for surface structures found in their experiments.