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Data assimilation for high dimensional nonlinear forecasting

New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 29, 2015 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): David Kelly (New York University, Courant Institute)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14399

Abstract

The prototypical problem of data assimilation is weather forecasting. The goal is to provide state predictions for nonlinear and extremely high dimensional models, the novelty is to determine how best to guide these predictions using the now vast amounts of observational data that is available to forecasters. Most data assimilation algorithms have been developed within the applied sciences, notably in meteorology. As a consequence these algorithms sit on little to no mathematical foundation, instead they are ad hoc methods whereby well-understood algorithms are tweaked to make them more suitable to the given problem. Nevertheless, numerical evidence suggests that these algorithms work - they often possess mathematically well understood properties, such as filter accuracy (tracking the right signal) and stability (ergodicity).

 

We will discuss two roles that mathematicians can play in this field: 1 - to develop understanding of the mathematics behind seemingly ad hoc forecasting algorithms and 2 - to use this understanding to propose new algorithms that are strongly backed by theory. 

 

This is based on several joint works with Andy Majda, Andrew Stuart and Xin Tong.   

Supplements
24883?type=thumb kelly-Notes 51.9 KB application/pdf Download
24884?type=thumb kelly-Talk 298 KB application/pdf Download
Video/Audio Files

14399

H.264 Video 14399.mp4 359 MB video/mp4 rtsp://videos.msri.org/data/000/024/688/original/14399.mp4 Download
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