Due to infection prevention measures, participation in events at the institute is presently not possible for guests.
Many events are currently organized online. Information on how to access these events can be found by clicking “more” below the respective entry.
- Monday, 03.05.2021, 15:00 (Online Event)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Assoc. Prof. Lars Ruthotto, Emory University, USA:
A machine learning framework for mean field games and optimal control
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We consider the numerical solution of mean field games and optimal control problems whose state space dimension is in the tens or hundreds. In this setting, most existing numercial solvers are affected by the curse of dimensionality (CoD). To mitigate the CoD, we present a machine learning framework that combines the approximation power of neural networks with the scalability of Lagrangian PDE solvers. Specifically, we parameterize the value function with a neural network and train its weight using the objective function with additional penalties that enforce the Hamilton Jacobi Bellman equations. A key benefit of this approach is that no training data is needed, e.g., no numerical solutions to the problem need to be computed before training. We illustrate our approach and its efficacy using numerical experiments. To show the framework's generality, we consider applications such as optimal transport, deep generative modeling, mean field games for crowd motion, and multi-agent optimal control.
- Tuesday, 04.05.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Maximilian Engel, FU Berlin:
Lyapunov exponents in random dynamical systems and how to find and use them
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This talk aims to give an overview on various notions of Lyapunov exponents (LEs) in random dynamical systems, that is, systems whose evolution in time is governed by laws exhibiting randomness: from finite-time LEs to classical asymptotic LEs and corresponding spectra up to LEs for processes conditioned on staying in bounded domains. We demonstrate how these notions, especially of a first, dominant LE, become relevant in the context of stochastic bifurcations, in finite and infinite dimensions.
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84203723799.
Freie Universität Berlin