Bayesian parameter identification in Cahn-Hilliard models for biological growth
This work provides a rigorous Bayesian foundation for parameter estimation in a specific biological growth model, but is incremental as it builds upon and improves existing analytical results.
The authors develop a Bayesian framework for parameter identification in a Cahn-Hilliard model of tumor growth, proving well-posedness of the posterior measure for both infinite-dimensional (full tumor) and finite-dimensional (tumor volume) observation settings. Numerical results with synthetic data demonstrate the approach using sequential Monte Carlo with tempering.
We consider the inverse problem of parameter estimation in a diffuse interface model for tumour growth. The model consists of a fourth-order Cahn-Hilliard system and contains three phenomenological parameters: the tumour proliferation rate, the nutrient consumption rate, and the chemotactic sensitivity. We study the inverse problem within the Bayesian framework and construct the likelihood and noise for two typical observation settings. One setting involves an infinite-dimensional data space where we observe the full tumour. In the second setting we observe only the tumour volume, hence the data space is finite-dimensional. We show the well-posedness of the posterior measure for both settings, building upon and improving the analytical results in [C. Kahle and K.F. Lam, Appl. Math. Optim. (2018)]. A numerical example involving synthetic data is presented in which the posterior measure is numerically approximated by the sequential Monte Carlo approach with tempering.