Particle Approximations For Partially Observed Fluid Dynamics Models

  • Professor Dan Crisan, Mathematics, Imperial College London
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KAUST

Fluid dynamics models are ubiquitous in a multitude of applications. One of the most important applications of fluid dynamics models is numerical weather prediction. Modern numerical weather prediction combines sophisticated nonlinear fluid dynamics models with increasingly accurate high-dimensional data. This process is called data assimilation and it is performed every day at all major operational weather centers across the world. Data assimilation (DA) requires massive computing capabilities as realistic atmosphere-ocean models typically have billions of degrees of freedom. I will give a short overview of the ongoing research that aims to drastically decrease the required DA computational effort by reducing the dimension of the models involved and using stochastic perturbations to account for the unresolved scales. The incorporation of observation data is done by using particle approximations suitably adapted to solve high-dimensional problems.

Abstract

Fluid dynamics models are ubiquitous in a multitude of applications. One of the most important applications of fluid dynamics models is numerical weather prediction. Modern numerical weather prediction combines sophisticated nonlinear fluid dynamics models with increasingly accurate high-dimensional data.  This process is called data assimilation and it is performed every day at all major operational weather centers across the world. Data assimilation  (DA) requires massive computing capabilities as realistic atmosphere-ocean models typically have billions of degrees of freedom. I will give a short overview of the ongoing research that aims to drastically decrease the required DA computational effort by reducing the dimension of the models involved and using stochastic perturbations to account for the unresolved scales. The incorporation of observation data is done by using particle approximations suitably adapted to solve high-dimensional problems.

Brief Biography

Dan Crisan is a Professor of Mathematics at Imperial College London. Crisan’s research lies at the interface between Mathematics Analysis and Probability Theory. He is particularly interested in studying macroscopic models such as solutions of partial differential equations through their microscopic and stochastic counterparts. Some of his key contributions relevant to the proposed research include: the theoretical justification for particle approximations for linear parabolic SPDEs; a sequential Monte Carlo method stable in the state space dimension; a refined analysis of the smoothness of solutions of semi-linear PDEs, a new McKean-Vlasov approximation for the Kushner-Stratonovich equation, well-posedness results for stochastic transport PDEs, etc. His research is acknowledged by the scientific community at large, as illustrated by his many invitations at pure/applied mathematics, engineering and statistics conferences. He is one of the pioneers of the application of particle filters in data assimilation.

Crisan first came to Imperial in 1995 as a postdoctoral fellow. After a brief spell at the Statistical Laboratory in Cambridge, Crisan returned to Imperial in 2000, where he was awarded a Governors' Lectureship. Since then, he has assiduously promoted Stochastic Analysis in the Department of Mathematics, across the College and beyond. In December 2002, Crisan initiated the Stochastic Analysis (SA) group at Imperial College London.  The SA group is now one of the largest and most successful research groups in the UK.

In 2013, Crisan became the Director of the newly founded Centre for Doctoral Training in the Mathematics of Planet Earth. For his work in establishing the Centre, Crisan was awarded the 2018 President’s Award for Excellence in Research Supervision. Crisan has worked continuously not just to ensure the success of the Centre but also to promote the new research area of Mathematics of Planet Earth. Crisan is one of the founding editors of the new series of Springer Briefs in Mathematics of Planet Earth. Weather, Climate, Oceans. Crisan is the recipient of a 2018 Chair of Excellence to held at Universidad Carlos III de Madrid.

Dan Crisan was appointed Senior Coordinator at the International Mathematics Olympiad (IMO) 2019. In 2019, the UK hosted the 60th edition of the International Mathematics Olympiad (IMO) see https://www.imo2019.uk.  The IMO is the largest and most prestigious of all of the international Olympiads. Initiated by Romania in 1959, the IMO has grown from the original seven countries to over a hundred to-date. The United Kingdom has participated since 1967 and has played host to the competition on two previous occasions (in 1979 and 2002). Dan Crisan was appointed Senior Coordinator also at IMO1999 and IMO2002.

Crisan is the current recipient of a £10 mil ERC Synergy grant held jointly with Bertrand Chapron (Ifremer), Darryl Holm (Imperial) and Etienne Memin (Inria). The grant is funding a large-scale multi-disciplinary project entitled Stochastic Transport in the Upper Ocean Dynamics. The project aims to produce a new systematic capability for dealing with the changing regimes of uncertainty in upper ocean fluid transport.

 http://www.springer.com/series/15250
 https://www.uc3m.es/ss/Satellite/UC3MInstitucional/en/PortadaMiniSiteA/1371224077923/Chairs_of_Excellence
 https://www.imperial.ac.uk/ocean-dynamics-synergy/

Presenters

Professor Dan Crisan, Mathematics, Imperial College London