Gaussian process modeling with applications to tumor growth

• Autor(a) principal: Silva, João Vitor de Oliveira
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/339
• topic: Câncer - Modelos matemáticos; Modelagem mecanística; Modelagem baseada em dados; Teoria bayesiana de decisão estatística; Processos gaussianos; CNPQ::CIENCIAS DA SAUDE::MEDICINA::CLINICA MEDICA::CANCEROLOGIA

Abstract Mechanistic models have been used widely as important tools for understanding and development in many areas of science and engineering. In particular, tumor growth models have provided a better understanding of how the disease evolves and helped in the development of therapies. This process incurs in the solution of an inverse problem. There are several methods dedicated to solving such problems, one of these is Bayesian inference. The difficulty of performing Bayesian inference or other methods is that, in general, they require repeated model evaluation. This may be computationally prohibitive for complex models, specially multiscale models. There are approximate Bayesian inference techniques, which reduce the overall computational time, although these may still be infeasible if the model is expensive to be evaluated. In order to alleviate the difficulty in this procedure, we propose the use of a surrogate (or metamodel). Our surrogate model is a Gaussian Process, a data-driven model recently used in machine learning and metamodeling context. This work reviews theoretical and practical aspects of Gaussian processes (GP) in a regression problem, discussing how to construct an adequate GP for a particular problem, covering recent developments in this area. We then define a GP surrogate model and combine it with an Approximate Bayesian Computation Markov-Chain Monte Carlo method, the ABC-MCMC method, for solving the inverse problem. We compare the standard and proposed approaches in two tumor growth models. Our results suggest that the proposed strategy is promising in terms of reducing the computational cost.