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CATEGORIES:Applied and Computational Analysis
SUMMARY:Data-driven schemes for high-dimensional Hamilton-
Jacobi-Bellman PDEs - Dante Kalise (Imperial)
DTSTART;TZID=Europe/London:20230221T150000
DTEND;TZID=Europe/London:20230221T160000
UID:TALK197779AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/197779
DESCRIPTION:Optimal feedback synthesis for nonlinear dynamics
-a fundamental problem in optimal control- is enab
led by solving fully nonlinear Hamilton-Jacobi-Bel
lman type PDEs arising in dynamic programming. Whi
le our theoretical understanding of dynamic progra
mming and HJB PDEs has seen a remarkable developme
nt over the last decades\, the numerical approxima
tion of HJB-based feedback laws has remained large
ly an open problem due to the curse of dimensional
ity. More precisely\, the associated HJB PDE must
be solved over the state space of the dynamics\, w
hich is extremely high-dimensional in applications
such as distributed parameter systems or agent-ba
sed models.\n\nIn this talk we will review recent
approaches regarding the effective numerical appro
ximation of very high-dimensional HJB PDEs via dat
a-driven schemes in supervised and semi-supervised
learning environments. We will discuss the use of
representation formulas as synthetic data generat
ors\, and different architectures for the value fu
nction\, such a polynomial approximation\, tensor
decompositions\, and deep neural networks.\n
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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