ME Special Seminar Series with Kody Law

1:00 pm on Tuesday, November 20, 2012
110 Cummington Mall, Room 245
The Department of Mechanical Engineering is pleased to announce:

Kody Law:
Accurate filtering for the Navier-Stokes Equation

University of Warwick

Filtering in the data assimilation context is often considered to be the reproduction of a point estimate of the state of a system from noisily observed data and knowledge of the underlying system, resulting in a continuous feedback control problem. This is in contrast to the probabilistic interpretation of the state as a random quantity, whose distribution reflecting our knowledge at a particular time is referred to as the filtering distribution, i.e. the distribution of state given the filtration generated by the random observations made up until the given time. We focus on the former case in which the model is know, i.e. the perfect model scenario. In the perfect model scenario two ideas drive accurate filtering: (i) observe enough low frequency information, and (ii) model variance inflation: trust the observations. In this talk I will illustrate this for the simplest filter, referred to as 3DVAR (perhaps more accurately called 2DVAR, if one then adapts 4DVAR to (2+1)DVAR) applied to the 2D Navier-Stokes equation, in the low and high frequency observation limits.

About the speaker:
Kody Law is a Postdoctoral Research Fellow at the Warwick Mathematics Institute at the University of Warwick. His current research focus is on data assimilation. He is also involved in bifurcation and stability analysis of nonlinear PDEs. His interest in data assimilation relates particularly to the accuracy and stability of filters for high-dimensional systems and the relationship to both nonlinear filtering as a sequential Bayesian inverse problem, on the one hand, and deterministic feedback control, on the other hand. Examples of systems which are currently of particular interest are fluid dynamical systems as related to numerical weather prediction and oceanography and also subsurface systems as related to subsurface reconstruction and oil recovery. He is generally interested in sequential, online, quantification of uncertainty in high-dimensional systems from both the probabilistic nonlinear filtering perspective, as well as the control theoretic perspective. Other such systems may arise, for example, as the discretization of a physical system governed by a PDE. His research in bifurcation and stability analysis is primarily applied to nonlinear wave equations and, in particular, nonlinear optical systems and Bose-Einstein condensates.

1 PM Tuesday, November 20th, 2012
110 Cummington Mall, Room 245

Pizza will be served at 12:45 pm.