5 papers
Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
Piotr Gwiazda, Alexey Kazarnikov, Anna Marciniak-Czochra +1
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due t…
Stochastic parabolic equations in Musielak-Orlicz spaces with discontinuous in time N-function
Piotr Gwiazda, Jakub Woźnicki, Aneta Wróblewska-Kamińska +1
We consider a stochastic parabolic partial differential equation with Dirichlet boundary conditions, multiplicative stochastic noise, and a monotone parabolic operator A. The growt…
Lipschitz stability for Bayesian inference in porous medium tissue growth models
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +3
We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive rela…
Rigorous derivation of magneto-Oberbeck-Boussinesq approximation with non-local temperature term
Piotr Gwiazda, Florian Oschmann, Aneta Wróblewska-Kamińska
We consider a general compressible, viscous, heat and magnetically conducting fluid described by the compressible Navier-Stokes-Fourier system coupled with induction equation. In p…
Operator splitting algorithm for structured population models on metric spaces
Carolin Lindow, Christian Düll, Piotr Gwiazda +2
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of…