相关论文: Bayesian parameter identification in Cahn-Hilliard…

Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the…

In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given…

Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models…

Predicting cancer dynamics under treatment is challenging due to high inter-patient heterogeneity, lack of predictive biomarkers, and sparse and noisy longitudinal data. Mathematical models can summarize cancer dynamics by a few…

This study presents a proof-of-concept for a novel Bayesian inverse method in a one-dimensional setting, aimed at proton beam therapy treatment verification. Our methodology is predicated on a hypothetical scenario wherein strategically…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding…

In this paper we perform an asymptotic analysis for two different vanishing viscosity coefficients occurring in a phase field system of Cahn-Hilliard type that was recently introduced in order to approximate a tumor growth model. In…

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…

In this work, we develop a structure-preserving numerical scheme for a Cahn-Hilliard-Darcy model that describes tumor growth in a fluid-saturated porous medium. First, we derive a physically consistent model from the general framework…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…

In this study, the applicability of generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We compute the (posterior) distribution of the critical hydrological parameters that are subject to…

We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type…

Bayesian inverse problem on an infinite dimensional separable Hilbert space with the whole state observed is well posed when the prior state distribution is a Gaussian probability measure and the data error covariance is a cylindric…

In this article, the solution of a statistical inverse problem $M = AU+\mathcal{E}$ by the Bayesian approach is studied where $U$ is a function on the unit circle $\mathbb{T}$, i.e., a periodic signal. The mapping $A$ is a smoothing linear…

In this study, we model avascular tumour growth in epithelial tissue. This can help us to get a macroscopic view of the interaction between the tumour with its surrounding microenvironment and the physical changes within the tumour…

The well known nonlinear model for describing the solid tumour growth [Byrne HM., et al. Appl Math Letters 2003;16:567-74] is under study using an approach based on Lie symmetries. It is shown that the model in the two-dimensional (in…