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SUMMARY:Data-driven schemes for high-dimensional Hamilton-Jacobi-Bellman P
 DEs - Dante Kalise (Imperial)
DTSTART:20230518T140000Z
DTEND:20230518T150000Z
UID:TALK198049@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:Optimal feedback synthesis for nonlinear dynamics\, a fundamen
 tal problem in optimal control\, is enabled by solving fully nonlinear Ham
 ilton-Jacobi-Bellman type PDEs arising in dynamic programming. While our t
 heoretical understanding of dynamic programming and HJB PDEs has seen a re
 markable development over the last decades\, the numerical approximation o
 f HJB-based feedback laws has remained largely an open problem due to the 
 curse of dimensionality. More precisely\, the associated HJB PDE must be s
 olved over the state space of the dynamics\, which is extremely high-dimen
 sional in applications such as distributed parameter systems or agent-base
 d models. In this talk we will review recent approaches regarding the effe
 ctive numerical approximation of very high-dimensional HJB PDEs via data-d
 riven schemes in supervised and semi-supervised learning environments. We 
 will discuss the use of representation formulas as synthetic data generato
 rs\, and different architectures for the value function\, such a polynomia
 l approximation\, tensor decompositions\, and deep neural networks.\n
LOCATION:Centre for Mathematical Sciences\, MR14
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