Upcoming Talks
This is a list of all upcoming talks for the next two weeks. Talks are from 3:454:45 p.m. in the Colloquium or Seminar Room, unless otherwise specified.

Oct27

Statistical reducedorder models and machine learningbased closure strategies for turbulent dynamical systemsDi QiPurdue UniversityLocation: https://meet.google.com/bkqsumwgxeTime: 03:45 PMColloquium Series
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The capability of using imperfect statistical reducedorder models to capture crucial statistics in complex turbulent systems is investigated. Much simpler and more tractable blockdiagonal models are proposed to approximate the complex and highdimensional turbulent dynamical equations using both parameterization and machine learning strategies. A systematic framework of correcting model errors with empirical information theory is introduced, and optimal model parameters under this unbiased information measure can be achieved in a training phase before the prediction. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the reducedorder model in various dynamical regimes of the flow field with distinct statistical structures. In addition, new machine learning strategies are proposed to learn the expensive unresolved processes directly from data.

Nov03

RONS: Reducedorder nonlinear solutions for PDEs with conserved quantitiesMohammad FarazmandNorth Carolina State UniversityLocation: https://meet.google.com/bkqsumwgxeTime: 03:45 PMColloquium Series
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Reducedorder models of timedependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a welldeveloped theory. However, more general models where the reduced solutions depend nonlinearly on timedependent variables have thus far been derived in an ad hoc manner. I introduce Reducedorder Nonlinear Solutions (RONS): a unified framework for deriving reducedorder models that depend nonlinearly on a set of timedependent variables. The set of all possible reducedorder solutions are viewed as a manifold immersed in the function space of the PDE. The variables are evolved such that the instantaneous discrepancy between reduced dynamics and the full PDE dynamics is minimized. This results in a set of explicit ordinary differential equations on the tangent bundle of the manifold. In the special case of linear parameter dependence, our reduced equations coincide with the standard Galerkin projection. Furthermore, any number of conserved quantities of the PDE can readily be enforced in our framework. Since RONS does not assume an underlying variational formulation for the PDE, it is applicable to a broad class of problems. I demonstrate its applications on a few examples including the nonlinear Schrodinger equation and Euler's equation for ideal fluids.

Nov05

TBAKostya MedynetsUSNA MathTime: 12:00 PMApplied Math Seminar