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Campillo-Funollet2018_Article_BayesianParameterIdentificatio.pdf (3.22 MB)

Bayesian parameter identification for Turing systems on stationary and evolving domains

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posted on 2023-06-09, 15:40 authored by Eduard Campillo-Funollet, Chandrasekhar VenkataramanChandrasekhar Venkataraman, Anotida Madzvamuse
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.

Funding

Coupling Geometric PDEs with Physics; ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES; EP/K032208/1

Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149

InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION

Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces; G0872; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/J016780/1

New predictive mathematical and computational models in experimental sciences; G1949; ROYAL SOCIETY; WM160017

History

Publication status

  • Published

File Version

  • Published version

Journal

Bulletin of Mathematical Biology

ISSN

0092-8240

Publisher

Springer Verlag

Issue

1

Volume

81

Page range

81-104

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Genome Damage and Stability Centre Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-10-29

First Open Access (FOA) Date

2018-10-29

First Compliant Deposit (FCD) Date

2018-10-29

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