I will discuss a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution of the backward Kolmogorov equation of the underlying dynamics on a basis adapted to the invariant measure. This approach allows one to evolve the probability distribution of non-trivial dynamical systems with equation-free modeling. I will also discuss nonparametric filtering methods, leveraging the diffusion forecast in Bayesian framework to initialize the forecasting distribution given noisy observations.
John Harlim is an associate professor of mathematics and meteorology at the Pennsylvania State University. He received Ph.D. in Applied Mathematics and Scientific Computation from University of Maryland in 2006. His research interests is applied mathematics related to data-driven estimation and prediction problems; this includes filtering multiscale dynamical systems, stochastic parameterization, uncertainty quantification, diffusion maps, non-parametric modeling.Co-hosted with Prof. Themis Sapsis.