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SUMMARY:Bayesian Uncertainty Quantification for Differential Equations - G
 irolami\, M (University of Warwick)
DTSTART:20140513T090000Z
DTEND:20140513T100000Z
UID:TALK52561@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:This talk will make a case for expansion of the role of Bayesi
 an statistical inference when formally quantifying uncertainty in computer
  models defined as systems of ordinary or partial differential equations b
 y adopting the perspective that implicitly defined infinite dimensional fu
 nctions representing model states are objects to be inferred probabilistic
 ally. \nI describe a general methodology for the probabilistic "integratio
 n" of differential equations via model based updating of a joint prior mea
 sure on the space of functions\, their temporal and spatial derivatives.  
 This results in a measure over functions reflecting how well they satisfy 
 the system of differential equations and corresponding initial and boundar
 y values. \nThis measure can be naturally incorporated within the Kennedy 
 and O'Hagan framework for uncertainty quantification and provides a fully 
 Bayesian approach to model calibration and predictive analysis.  \n\nBy ta
 king this probabilistic viewpoint\, the full force of Bayesian inference c
 an be exploited when seeking to coherently quantify and propagate epistemi
 c uncertainty in computer models of complex natural and physical systems. 
  A broad variety of examples are provided to illustrate the potential of t
 his framework for characterising discretization uncertainty\, including in
 itial value\, delay\, and boundary value differential equations\, as well 
 as partial differential equations.  I will also demonstrate the methodolog
 y on a large scale system\, by modeling discretization uncertainty in the 
 solution of the Navier-Stokes equations of fluid flow\, reduced to over 16
 \,000 coupled and stiff ordinary differential equations.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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