ArticleBulletin of mathematical biology2019
Bayesian Parameter Identification for Turing Systems on Stationary and Evolving Domains.
Article in Bulletin of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Persistent Homology Classifies Parameter Dependence of Patterns in Turing Systems.Bulletin of mathematical biology · 2025Article
- Actin network heterogeneity tunes activator-inhibitor dynamics at the cell cortex.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns.iScience · 2024Article
- Learning system parameters from turing patterns.Machine learning · 2023Article
- Predicting and forecasting the impact of local outbreaks of COVID-19: use of SEIR-D quantitative epidemiological modelling for healthcare demand and capacity.International journal of epidemiology · 2021Article
- Bespoke Turing Systems.Bulletin of mathematical biology · 2021Article
- Optogenetic Tuning Reveals Rho Amplification-Dependent Dynamics of a Cell Contraction Signal Network.Cell reports · 2020Article
- Computational modeling of therapy on pancreatic cancer in its early stages.Biomechanics and modeling in mechanobiology · 2020Article
- A mathematical understanding of how cytoplasmic dynein walks on microtubules.Royal Society open science · 2018Article
- Data-Driven Identification of Rational Nonlinear Dynamics in Biochemical Networks via an Implicit Singular Value Decomposition Based Framework.IET systems biologyArticle
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Authors and funding
3 authors.
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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.
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