Campillo-Funollet2018_Article_BayesianParameterIdentificatio.pdf (3.22 MB)
Bayesian parameter identification for Turing systems on stationary and evolving domains
journal contribution
posted on 2023-06-09, 15:40 authored by Eduard Campillo-Funollet, Chandrasekhar VenkataramanChandrasekhar Venkataraman, Anotida MadzvamuseAnotida MadzvamuseIn 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 BiologyISSN
0092-8240Publisher
Springer VerlagExternal DOI
Issue
1Volume
81Page range
81-104Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Genome Damage and Stability Centre Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-10-29First Open Access (FOA) Date
2018-10-29First Compliant Deposit (FCD) Date
2018-10-29Usage metrics
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