Applied Mathematics Colloquium
Quantifying uncertainty and improving statistical predictions for partially observed turbulent dynamical systems
In the talk I will give an overview of my research on a newly emerging stochastic-statistical framework which allows for information-theoretic quantification of uncertainty and mitigation of model error in imperfect statistical predictions of complex multi-scale dynamics. Two important examples used to highlight these issues will be concerned with (i) existence of 'information' barriers to imperfect model improvement and (ii) real-time 'stochastic superresolution' for estimation of the relevant unresolved processes in sparsely observed turbulent systems. Open mathematical and practical problems for future research will also be discussed.