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Mathematics and Deep Learning Collective

Author: Lona

Dr. Levon Nurbepkyan, from UCLA

Title: A neural network approach for high-dimensional real-time optimal control

Abstract: Due to fast calculation at the deployment, neural networks (NN) are attractive for real-time applications. I will present one possible approach for training NN to synthesize real-time controls. A key aspect of our method is the combination of the following features:

  1. No data generation and fitting
  2. Direct optimization of trajectories
  3. The correct structural ansatz for the approximations of optimal control

With these techniques, we can solve problems in hundreds of dimensions. We also find some unexpected generalization properties. The talk is based on two recent papers and

Brief bio: I am currently an Assistant Adjunct Professor at the Department of Mathematics at UCLA. I obtained my Ph.D. in the framework of UT Austin — Portugal CoLab under the supervision of Professors Diogo Gomes and Alessio Figalli. My research interests include calculus of variations, optimal control theory, mean-field games, partial differential equations, mathematics applied to machine learning, dynamical systems, and shape optimization problems.  I have been a Senior Fellow at the Institute for Pure and Applied Mathematics (IPAM) at UCLA for its Spring 2020 Program on High Dimensional Hamilton-Jacobi PDEs and a Simons CRM Scholar at the Centre de Recherches Mathématiques (CRM) at the University of Montreal for its Spring 2019 Program on Data Assimilation: Theory, Algorithms, and Applications.

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