Prof. Dimitris Giannakis
Assistant Professor, Courant Insitute of Mathematical Sciences, NYU
Extracting and predicting spatiotemporal patterns from data with dynamics-adapted kernels
Friday, March 6, 2015, 2:00pm to 3:00pm | Room 1-390
Kernel methods provide an attractive way of extracting features from data by biasing their geometry in a controlled manner. In this talk, we discuss a family of kernels for dynamical systems featuring an explicit dependence on the generator of the dynamics operating in the phase-space manifold, estimated empirically through finite differences of time-ordered data samples. The associated diffusion operator for data analysis is adapted to the dynamics in that it generates diffusions along the integral curves of the dynamical vector field. We present applications to dimension reduction and timescale separation in toy dynamical systems and comprehensive climate models. We also discuss a technique for analog forecasting based on these kernels. In this nonparametric forecasting technique (originally introduced by Lorenz in 1969), kernels are used to create weighted ensembles of states (analogs) with high similarity to the initial data from a record of historical observations, and the future values of observables are predicted from the historical evolution of the ensemble.
Dimitris Giannakis is an Assistant Professor of Mathematics at the Courant Institute of Mathematical Sciences, NYU. He is also affiliated with Courant's Center for Atmosphere Ocean Science (CAOS). He received BA and MSci degrees from the University of Cambridge in 2001, and a PhD degree from the University of Chicago in 2009. Prior to joining Courant and CAOS as faculty he was a postdoctoral researcher there from 2009-2012. Giannakis' research work is at the interface between applied mathematics and climate atmosphere ocean science. His primary research interests are in geometrical data analysis and statistical modeling of complex systems. He has applied these tools in topics including idealized dynamical systems, ocean and sea ice variability on seasonal to interannual timescales, and organized atmospheric convection.