BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Explicit stabilised Runge-Kutta methods and their application to B
 ayesian inverse problems  - Kostas Zygalakis\, University of Edinburgh
DTSTART:20190308T160000Z
DTEND:20190308T170000Z
UID:TALK115927@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:The concept of Bayesian inverse problems provides a coherent m
 athematical and algorithmic framework that enables researchers to combine 
 mathematical models with the (often vast) datasets routinely available tod
 ay in many fields of engineering science and technology. The ability to so
 lve such inverse problems depends crucially on the efficient calculation o
 f quantities relating to the posterior distribution\, giving rise to compu
 tationally challenging high dimensional optimization and sampling problems
 . In this talk\, we will connect the corresponding optimization and sampli
 ng problems to the large time behaviour of solutions to (stochastic) diffe
 rential equations. Establishing such a connection allows utilising existin
 g knowledge from the field of numerical analysis of differential equations
 . In particular\, numerical stability is key for a good performing optimiz
 ation or sampling algorithm since the larger the time-step used while the 
 limiting behaviour of the underlying differential equation is preserved\, 
 the more computationally efficient an algorithm is. With this in mind we w
 ill explore the applicability of explicit stabilised Runge-Kutta methods f
 or optimization and sampling problems\; These methods are optimal in terms
  of their stability properties within the class of explicit integrators an
 d we will show that when used as optimization methods they match the optim
 al convergence rate of the conjugate gradient method for quadratic optimiz
 ation problems. Numerical investigations indicate  that in the general cas
 e they are able to outperform state of the art optimization methods like  
  Nesterov's accelerated method. In the case of sampling\, we will investig
 ate their applicability to Bayesian inverse problems arising in computatio
 nal imaging. An additional complexity arises there due to the fact that ma
 ny of them contain non-differentiable terms\, which when regularised lead 
 to extra stiffness\, hence making explicit stabilised methods even more su
 itable for these problems as illustrated by a range of numerical experimen
 ts that show that for the same computational cost as current state of the 
 arts methods\, explicit stabilised methods deliver much better MCMC sample
 s. \n\nThis is joint work with Armin Eftekhari (EPFL)\, Bart Vandereycken 
 (Geneva)\, Gilles Vilmart (Geneva)\, Marcelo Pereyra (Heriot-Watt) and Lui
 s Vargas (Edinburgh)
LOCATION:MR12
END:VEVENT
END:VCALENDAR