Scientific Computing Group Seminars - Detail View

Speaker: Y. Park

Affiliation: University of Illinois, Urbana-Champagne

Talk Title: Efficient estimation of complex systems

Invited by: George Karniadakis

Time: Aug. 28 2009 11 a.m.

Location: 182 George Street, Room 110

Abstract:

Multiscale properties are ubiquitous in science and engineering with regard to both space and time. Due to limited knowledge and technological capacity however, modeling in the past had been concerned with the macroscopic - coarse grained - nature of physical phenomena which were easily observable. In parallel with unprecedented computational power and technological innovations, access to formerly ignored microscopic regimes has opened up recently. As the modeling in each scale has been maturing, the development of new techniques capable of commanding both scales in harmony has come into the spotlight of the scientific community. On the other hand, data has been used as an indispensable resource for validation and verification of modeling. Proper and accurate models can only be obtained through their combination with data. Especially in the recent era, vast amounts of data has been produced via various sources, from high-resolution microscopy, network-connected sensor arrays to satellites, all with a wide range of spatial and time scales. To deal with such an onslaught of data, it is necessary to have a new framework capable of harnessing and processing these data with multiscale models. The theory of nonlinear filtering forms the framework in our study for the assimilation of data into multiscale models. When the rates of change of different model variables differ by orders of magnitude, efficient data assimilation can be accomplished by constructing nonlinear filtering equations for the coarse-grained signal. We consider the conditional law of a signal given the observations in a multiscale context. In particular, we study how scaling interacts with filtering via stochastic averaging. Our main result is a mathematically rigorous and computationally efficient approximation for high dimensional nonlinear filtering. Our result is applied to the electric power system whose daily operations must be guarded against failures due to natural disasters, rogue attacks and other unexpected conditions. One of the central challenges in current power system operations is to develop a better estimation scheme which is able to combine large dimensional systems with large volumes of data within a given response time that meets operational demands for health monitoring. We show that our scheme can be effectively used for this significant and challenging problem by providing a near real-time condition assessment for ``extreme events''.