Neural network-based approaches for multiscale modelling of topological defects

Prof. Dr. Friederike Schmid
Dr. Karin Everschor-Sitte

We propose to develop artificial neural network (ANN)-based tools for modelling topological defects on multiple scales. Specifically, tools will be designed to bridge between microscopic representations, where defects emerge as nonlinear excitations, and defect-particle representations, where defects are treated as explicit objects. The coarse-grained representation at the defect-particle level (the defect-particle model) will ideally be a dynamic neural network, but we will also consider equation-based parametrized models. First, we will separately address the problem of mapping microscopic representations onto defect-particle representations and the problem of backmapping from given defect-particle configurations to microscopic configurations. Then, we will explore schemes where defect-particle representations and microscopic representations evolve concurrently such that the defect-particle model is constantly updated on the fly. We will develop and test our methods using the example of topological defects in the XY model, in nematic liquid crystals, and finally magnetic skyrmions. Our results will provide a deeper understanding how information is gained or lost in the learning, coarsening and refining processes thereby allowing to reveal and predict processes on the microscopic level based on macroscopic observed data.