Bayesian parameter identification for Turing systems on stationary and evolving domains

Campillo-Funollet, Eduard, Venkataraman, Chandrasekhar and Madzvamuse, Anotida (2018) Bayesian parameter identification for Turing systems on stationary and evolving domains. Bulletin of Mathematical Biology. ISSN 0092-8240

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In this study, we apply the Bayesian paradigm for parameter identification to a well-studied semi-linear reaction-difusion system with activatordepleted 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. While 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 wellposedness 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
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Genome Damage and Stability Centre
Subjects: Q Science > QA Mathematics
Depositing User: Joshua Jenkin
Date Deposited: 29 Oct 2018 16:48
Last Modified: 29 Mar 2019 18:30

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Mathematical Modelling and Analysis of Spatial Patterning on Evolving SurfacesG0872EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/J016780/1