Prof. Nan Chen
Assistant Professor, Department of Mathematics, University of Wisconsin-Madison
A Nonlinear Conditional Gaussian Framework for Prediction, State Estimation and Uncertainty Quantification in Complex Dynamical System
Friday, April 5, 2019, 11:00am to 12:00pm | Room 5-314
A nonlinear conditional Gaussian framework for extreme events prediction, state estimation (data assimilation) and uncertainty quantification in complex dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the models within this framework remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction.
In the first part of this talk, the general framework of the nonlinear conditional Gaussian systems, including a gallery of examples in geophysics, fluids, engineering, neuroscience and material science, will be presented. This is followed by its wide applications in developing the physics-constrained data-driven nonlinear models and the stochastic mode reduction. In the second part, an efficient statistically accurate algorithm is developed for solving the Fokker-Planck equation in large dimensions, which is an extremely important and challenging topic in prediction, data assimilation and uncertainty quantification. This new efficient algorithm involves a novel hybrid strategy for different subspaces, a judicious block decomposition and statistical symmetry. Rigorous mathematical analysis shows that this method is able to overcome the curse of dimensionality. In the third part of this talk, a low-order model within the nonlinear conditional Gaussian framework is developed to predict the intermittent large-scale monsoon extreme events in nature. The nonlinear low-order model shows higher prediction skill than the operational models and it also succeeds in quantifying the uncertainty in prediction. Other applications of this nonlinear conditional Gaussian framework, such as assimilating multiscale turbulent ocean flows and parameter estimation, will be briefly mentioned at the end of the talk.
Nan Chen is now an assistant professor in the mathematics department of the University of Wisconsin-Madison (UW-Madison). Nan Chen got his PhD from Courant Institute of Mathematical Sciences at New York University (NYU) in 2016. Then he stayed at NYU as a postdoc before he joined UW-Madison. Nan Chen's research interests include data assimilation, uncertainty quantification and prediction for complex turbulent dynamical systems. He also works on developing new dynamical and statistical models for different atmosphere and ocean phenomena, such as the El Nino Southern Oscillation and Monsoon.