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"Information-theoretic control of wall-bounded turbulence"
Gonzalo Arranz Fernandez
MIT ACDL
Abstract: Information theory is the science about the laws governing information or, in other words, the mathematics of message communications. Since its original formulation by Shannon in 1948, information theory has matured into a much discipline applicable to engineering, biology, medical science, sociology, psychology… The success of information theory relies on the notion of information as a fundamental property of physical systems, closely tied to the restrictions and possibilities of the laws of physics. In the present talk, we formulate the problem of control of a dynamical system from an information theoretic perspective; by envisioning the tandem sensor-actuator as a device aimed at reducing the unknown information associated with the state of the system to be controlled. The proposed framework is then applied to find the optimal parameters for the opposition-flow control in a turbulent channel flow. The design parameters are the wall-normal sensor location and the actuator amplitude of the wall jet. It is shown that maximum drag reduction is achieved for controllers with maximum mutual information and minimum Kullback-Leibler divergence.
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"Low-rank ensemble Kalman filtering with applications in fluid dynamics"
Ricardo Miguel Baptista
MIT ACDL
Abstract: At the core of filtering problems for non-Gaussian state-space models is a challenging Bayesian inference step. The ensemble Kalman filter (EnKF) is a workhorse inference algorithm that is commonly used in geophysical applications, such as numerical weather prediction. While the EnKF is robust for high-dimensional states, it relies on ad-hoc forms of regularization. Localization is one regularization method that suppresses state correlations at long distances. For problems with long-range physical interactions, however, distance-based localization is not suitable. In this presentation, we propose a regularization technique that performs the Bayesian inference step in a low-dimensional subspace of the states using projected observations. We show that its equivalence to using a low-rank factorization of the Kalman gain and we demonstrate its benefit for estimating vortex dynamics and turbulent flow. Finally, we comment on the broader utility of this dimension reduction technique for nonlinear ensemble filtering methods.