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Distinguished Lecture:

Andy Majda
Courant Institute of Mathematical Sciences
New York University

5.15-6.15pm Thursday 16th May

Title: Particle Filters and Finite Ensemble Kalman Filters in Large Dimensions: Theory, Applied Practice, and New Phenomena

Abstract:

The filtering and predictive skill for turbulent signals is often limited by the lack of information about the true dynamics of the system and by our inability to resolve the assumed dynamics with sufficiently high resolution using the current computing power. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the underlying multiscale structure, applying the full Kalman filtering procedures only to the large scale variables, and estimating the small scale variables with proper statistical strategies, including multiplicative inflation, representation model error in the observations, and crude localization. A new error analysis framework for different reduced random Kalman filters is established, The classical tools for Kalman filters can be used as a-priori performance criteria for the reduced filters. In applications, these criteria guarantee the reduced filters are robust, and accurate for small noise systems. They also shed light on how to tune the reduced filters for stochastic turbulence. A new class of particle filters, clustered particle filters, is also introduced for high-dimensional nonlinear systems. The clustered particle filter captures non-Gaussian features of the true signal which are typical in complex nonlinear dynamical systems such as geophysical systems.