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SUMMARY:A unifying paradigm for bringing together multimodal data and phys
 ics using information field theory - Ilias Bilionis (Purdue University)
DTSTART:20230731T133000Z
DTEND:20230731T143000Z
UID:TALK202396@talks.cam.ac.uk
DESCRIPTION:Information field theory (IFT) is Bayesian statistics for fiel
 ds (a.k.a. functions of space and time). It uses the same mathematics foun
 d in statistical field theory and quantum field theory\, namely functional
  integration or Feynman path integrals. IFT starts by imposing a prior pro
 bability measure over the space of physical fields (e.g.\, temperature\, p
 ressure\, strain\, stress). Then\, one constructs a likelihood function th
 at models the measurement process to connect the fields to the available d
 ata. Finally\, one uses Bayes&rsquo\; rule to build a posterior over the s
 pace of physical fields\, which they proceed to characterize either analyt
 ically (see Feynman diagrams) or numerically. IFT has been used successful
 ly in various field reconstruction problems\, primarily astrophysical appl
 ications. In this talk\, we will discuss how IFT can be used to perform un
 certainty quantification tasks in physical problems governed by ordinary a
 nd partial differential equations. We will show how one can 1) use knowled
 ge of the governing equations to construct suitable prior measures over th
 e space of fields\; 2) sample from the fields&rsquo\; posterior numericall
 y via advanced Markov chain Monte Carlo and variational inference without 
 the need to call a numerical solver\; and 3) sample from the posterior of 
 any physical parameters\, initial conditions\, boundary conditions\, and s
 ource terms without the need to evaluate a normalization constant. The met
 hod offers several potential advantages compared to traditional uncertaint
 y quantification techniques. The approach has a mechanism for quantifying 
 the model-form uncertainty. It naturally fuses data from multiple modaliti
 es and elegantly deals with ill-posed problems (e.g.\, missing boundary co
 nditions).
LOCATION:Seminar Room 1\, Newton Institute
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