time series analysis; discrete stochastic processes; graph inference; adaptive numerical methods; high performance computing; multiscale processes; Markov processes; transfer operator
(2013), Low frequency variability in a coupled ocean-sea ice general circulation model of the Southern Ocean., in ANZIAM J.
, 54, 200.
(2013), An adaptive Markov chain Monte Carlo approach to time series clustering of processes with regime transition behavior., in SIAM Journal of Multiscale Modeling and Simulation
(2013), Changes in the meta-stability of the mid-latitude Southern Hemisphere circulation and the utility of non-stationary cluster analysis and split flow blocking indices as diagnostic tools., in Journal of Atmospherical Science
(2013), Intrinsic and Forced Modes of Low Frequency Variability in Simulated Southern Ocean and Sea Ice Dynamics., in Ocean Modelling
(2013), The meta-stability of the mid-latitude Southern Hemisphere circulation., in ANZIAM J.
, 54, 233.
(2012), Information Theory, Model Error, and Predictive Skill of Stochastic Models for Complex Nonlinear Systems, in Physica D
, 241(20), 1735-1752.
(2012), Supervised Learning Approaches to Classify Stratospheric Warming Events, in Journal of Atmospherical Sciences
, 69, 1824-1840.
(2011), Nonstationarity in Multifactor Models of Discrete Jump Processes, Memory, and Application to Cloud Modeling, in JOURNAL OF THE ATMOSPHERIC SCIENCES
, 68(7), 1493-1506.
, Analysis of persistent non-stationary time series and applications, in CAMCOS
, 7(2), 175-229.
, Discrete non-homogenous and non-stationary logistic and Markov regression models for spatio-temporal data with unresolved external influences., in Communications in Applied Mathematics and Computational Science
, On analysis of nonstationary categorical data time series: dynamical dimension reduction, model selection and applications to computational sociology., in SIAM Mult. Mod. Sim
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 ofthe 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 bythe 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.