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Bayesian Parameter Identification for Turing Systems on Stationary and Evolving Domains.

Eduard Campillo-Funollet1, Chandrasekhar Venkataraman2, Anotida Madzvamuse2

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Summary
This summary is machine-generated.

This study introduces a Bayesian approach for identifying parameters in reaction-diffusion systems, even on evolving domains. This method rigorously handles uncertainty and provides a full probability distribution for parameters, enhancing scientific modeling.

Keywords:
Bayesian inverse problemsInverse problemsMarkov chain Monte CarloParameter identificationPattern formationReaction–diffusionTuring instability

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Area of Science:

  • Mathematical Biology
  • Computational Science
  • Chemical Kinetics

Background:

  • Reaction-diffusion systems are crucial for modeling biological and chemical processes.
  • Parameter identification in these systems is complex, especially on dynamic domains.
  • Existing methods often lack rigorous uncertainty quantification.

Purpose of the Study:

  • To apply the Bayesian paradigm for parameter identification in reaction-diffusion systems.
  • To develop a mathematically rigorous framework for inverse problems on stationary and evolving domains.
  • To incorporate prior knowledge of uncertainty into parameter estimation.

Main Methods:

  • Bayesian inference for parameter identification.
  • Analysis of semi-linear reaction-diffusion systems with activator-depleted kinetics.
  • Mathematical framework for inverse problems, including well-posedness proofs.
  • Numerical approximation using parallelized algorithms for high-performance computing.

Main Results:

  • A rigorous Bayesian framework for parameter identification in reaction-diffusion systems.
  • Successful application to both stationary and evolving domains.
  • Demonstration of incorporating prior uncertainty in observations and parameters.
  • Proof of well-posedness for the inverse problem based on forward problem solutions.

Conclusions:

  • The Bayesian approach offers a robust method for parameter identification in complex reaction-diffusion systems.
  • This framework effectively handles uncertainty and provides comprehensive parameter distributions.
  • The method is applicable to dynamic systems and computationally feasible with high-performance computing.