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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:20230518T150000
DTEND;TZID=Europe/London:20230518T160000
UID:TALK198049AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198049
DESCRIPTION:Optimal feedback synthesis for nonlinear dynamics\
, a fundamental problem in optimal control\, is en
abled by solving fully nonlinear Hamilton-Jacobi-B
ellman type PDEs arising in dynamic programming. W
hile our theoretical understanding of dynamic prog
ramming and HJB PDEs has seen a remarkable develop
ment over the last decades\, the numerical approxi
mation of HJB-based feedback laws has remained lar
gely an open problem due to the curse of dimension
ality. More precisely\, the associated HJB PDE mus
t be solved over the state space of the dynamics\,
which is extremely high-dimensional in applicatio
ns such as distributed parameter systems or agent-
based models. In this talk we will review recent a
pproaches regarding the effective numerical approx
imation of very high-dimensional HJB PDEs via data
-driven 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 fun
ction\, such a polynomial approximation\, tensor d
ecompositions\, and deep neural networks.\n
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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