AnaGraph - Adaptive numerical methoda for nonstationary time series analysis of time-dependent graphs in context of dynamical systems

This project AnaGraph is concerned with the development of adaptive numerical strategies for time series analysis and optimization in very large nonstationary graphs, i. e., graphs with the time-varying topology and weights of the edges. The information about the temporal changes of the considered graphs is assumed to be given implicitly through some (possibly incomplete) time series of graph observables. To achieve the main aim of the project, nonstationary persistency-regularized variational formulation of the Markovian inference problem recently developed by the applicant in context of discrete graph inference (for directly observable low-dimensional dynamical processes on small graphs) will be combined with an appropriate dimension reduction strategy and information theory concepts to allow for analysis of large nonstationary graph dynamics under influence of external factors. Adaptive numerical inference methods will be implemented using concepts from PDE numerics and tested on realistic climatological and financial time series.