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DynamIC Seminars (Complete List)

Name Title Date Time Room
Andrei Agrachev (SISSA, Trieste)Control of Diffeomorphisms with Applications to Deep LearningAbstract: Abstract: Given a control system on a smooth manifold M, any admissible control function generates a flow, i.e. a one-parametric family of diffeomorphisms of M. We give a sufficient condition for the system that guarantees the existence of an arbitrary good uniform approximation of any isotopic to the identity diffeomorphism by an admissible diffeomorphism and provide simple examples of control systems on \mathbb R^n, \mathbb T^n and \mathbb S^2 that satisfy this condition. This work is a joint work with A. Sarychev (Florence) motivated by the deep learning of artificial neural networks treated as a kind of interpolation technique. Tuesday, 26 January 2021 13:00 Online
Armen Shirikyan (Université de Cergy-Pontoise)A simple mixing criterion for random dynamical systems and an applicationAbstract: A well-known fact from the theory of stochastic differential equations on a compact manifold is that the validity of Hörmander's condition for the vector fields implies the uniqueness of a stationary measure and its exponential stability in the total variation metric. We study this problem in an abstract setting for a Markovian random dynamical system in a compact metric space. It is proved that the global controllability to a point and solid controllability from that point imply the uniqueness and exponential mixing of a stationary measure, provided that the noise satisfies a mild non-degeneracy hypothesis. The result is illustrated on a differential equation with random coefficients on a compact manifold. We shall also discuss briefly a generalisation of the abstract result that is applicable to a class of randomly forced PDEs. Tuesday, 2 February 2021 13:00 Online
Kathrin Padberg-Gehle (Leuphana University of Lüneburg)Data-based analysis of Lagrangian transport Abstract: Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterisation of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational or transfer operator based schemes require full knowledge of the flow field or at least high resolution trajectory data, this information may not be available in applications. In this talk, we review different spatio-temporal clustering approaches and show how these can be used to identify coherent behaviour in flows directly from Lagrangian trajectory data. We demonstrate the applicability of these methods in a number of example systems, including geophysical flows and turbulent convection. Tuesday, 9 February 2021 13:00 Online

DynamIC Workshops and Mini-Courses (Complete List)

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Short-term DynamIC Visitors (Complete List)

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