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SUMMARY:Uncertainty-Aware Numerical Solutions of ODEs by Bayesian Filterin
 g - Hans Kersting\, INRIA Paris
DTSTART:20210216T150000Z
DTEND:20210216T160000Z
UID:TALK157396@talks.cam.ac.uk
CONTACT:96082
DESCRIPTION:Numerical approximations can be regarded as statistical infere
 nce\, if one interprets the solution of the numerical problem as a paramet
 er in a statistical model whose likelihood links it to the information (`d
 ata') available from evaluating functions. This view is advocated by the f
 ield of Probabilistic Numerics and has already yielded two successes: Baye
 sian Optimization and Bayesian Quadrature. In an analogous manner\, we con
 struct a Bayesian probabilistic-numerical method for ODEs. To this end\, w
 e construct a probabilistic state space model for ODEs which enables us to
  borrow the machinery of Bayesian filtering. This unlocks the application 
 of all Bayesian filters from signal processing to ODEs\, which we name ODE
  filters. We theoretically analyse the convergence rates of the most eleme
 ntary one\, the Kalman ODE filter and discuss its uncertainty quantificati
 on. Lastly\, we demonstrate how employing these ODE filters as forward sim
 ulators engenders new ODE inverse problem solvers that outperform its clas
 sical 'likelihood-free' counterparts.
LOCATION:https://us02web.zoom.us/j/86046826779?pwd=RUZCVGxzdDMrRDN2bDJEUkk
 1NUVyUT09
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