This talk investigates the use of neural networks (NNs) as discrete approximations of first order nonlinear hyperbolic partial differential equations (PDEs). Two approaches are considered. The first is a supervised approach, performed on solutions of a training set composed of Riemann problems. The second approach, unsupervised, follows the physically inspired neural network (PINN) approach, in which a loss function based on the initial PDE is used to train the neural network. When available, semi-explicit solutions are used for validation (i.e. Lax-Hopf formula), which enables the comparison of these two approaches against classical numerical schemes (i.e. Lax-Friedrichs, Godunov, ENO, WENO, discrete Galerkin, etc.). The need of the Kruzhkov entropy condition is discussed in the context of unsupervised learning. Efficiency of methods (accuracy, computational cost) are discussed. Finally, the supervised approach is demonstrated on field data collected by a drone (Berkeley Deep Drive dataset); predictive capabilities of the supervised approach is assessed with success in comparison to all other discretizations of the underlying PDEs. Applications of the methods are finally presented in the context of mixed-autonomy traffic in which self-driving vehicles are used to control the entirety of traffic.
Biography
Alexandre Bayen is the Associate Provost for Moffett Field Program Development at UC Berkeley, and the Liao-Cho Professor of Engineering at UC Berkeley. He is a Professor of Electrical Engineering and Computer Science, and Civil and Environmental Engineering. From 2014 - 2021, he served as the Director of the Institute of Transportation Studies at UC Berkeley (ITS). He is also a Faculty Scientist in Mechanical Engineering, at the Lawrence Berkeley National Laboratory (LBNL). He received the Engineering Degree in applied mathematics from the Ecole Polytechnique, France, in 1998, the M.S. and Ph.D. in aeronautics and astronautics from Stanford University in 1999 and 2004, respectively. He was a Visiting Researcher at NASA Ames Research Center from 2000 to 2003. Between January 2004 and December 2004, he worked as the Research Director of the Autonomous Navigation Laboratory at the Laboratoire de Recherches Balistiques et Aerodynamiques, (Ministere de la Defense, Vernon, France), where he holds the rank of Major. He has been on the faculty at UC Berkeley since 2005. Bayen has authored five books and over 300 articles in peer reviewed journals and conferences. He is the recipient of the Ballhaus Award from Stanford University, 2004, of the CAREER award from the National Science Foundation, 2009 and he is a NASA Top 10 Innovators on Water Sustainability, 2010. His projects Mobile Century and Mobile Millennium received the 2008 Best of ITS Award for ‘Best Innovative Practice’, at the ITS World Congress and a TRANNY Award from the California Transportation Foundation, 2009. Bayen is the recipient of the Presidential Early Career Award for Scientists and Engineers (PECASE) award from the White House, 2010. He is also the recipient of the Okawa Research Grant Award, the Ruberti Prize from the IEEE, and the Huber Prize from the ASCE.
