A new network approach to Bayesian inference in partial differential equations

Dominic Kohler, Youssef M. Marzouk, Johannes Müller, Utz Wever

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state-discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network. In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen-Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition.

Original languageEnglish
Pages (from-to)313-329
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Volume104
Issue number5
DOIs
StatePublished - 2 Nov 2015

Keywords

  • Boyen-Koller algorithm
  • Cellular probabilistic automata
  • Dynamic Bayesian networks
  • Hyperbolic
  • Inverse
  • Partial differential equations
  • Probabilistic methods

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