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Bayesian Parameter Identification for Turing Systems on Stationary and Evolving Domains

Campillo-Funollet, Eduard, Venkataraman, Chandrasekhar, Madzvamuse, Anotida (2019) Bayesian Parameter Identification for Turing Systems on Stationary and Evolving Domains. Bulletin of Mathematical Biology, 81 (1). pp. 81-104. ISSN 0092-8240. E-ISSN 1522-9602. (doi:10.1007/s11538-018-0518-z) (KAR id:90468)

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Official URL:
https://doi.org/10.1007/s11538-018-0518-z

Abstract

In this study, we apply the Bayesian paradigm for parameter identification to a well-studied semi-linear reaction–diffusion system with activator-depleted reaction kinetics, posed on stationary as well as evolving domains. We provide a mathematically rigorous framework to study the inverse problem of finding the parameters of a reaction–diffusion system given a final spatial pattern. On the stationary domain the parameters are finite-dimensional, but on the evolving domain we consider the problem of identifying the evolution of the domain, i.e. a time-dependent function. Whilst others have considered these inverse problems using optimisation techniques, the Bayesian approach provides a rigorous mathematical framework for incorporating the prior knowledge on uncertainty in the observation and in the parameters themselves, resulting in an approximation of the full probability distribution for the parameters, given the data. Furthermore, using previously established results, we can prove well-posedness results for the inverse problem, using the well-posedness of the forward problem. Although the numerical approximation of the full probability is computationally expensive, parallelised algorithms make the problem solvable using high-performance computing.

Item Type: Article
DOI/Identification number: 10.1007/s11538-018-0518-z
Uncontrolled keywords: Bayesian inverse problems; Parameter identification; Inverse problems; Markov chain Monte Carlo; Reaction–diffusion; Pattern formation; Turing instability
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Amy Boaler
Date Deposited: 29 Sep 2021 14:24 UTC
Last Modified: 30 Sep 2021 08:55 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/90468 (The current URI for this page, for reference purposes)
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