Related papers: Space-time multilevel quadrature methods and their…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
The Extracellular-Membrane-Intracellular (EMI) model is a novel mathematical framework for cardiac electrophysiology simulations. The EMI model provides a more detailed description of the heart's electrical activity compared to traditional…
We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory…
The electrocardiogram (ECG) is a well-known technique used to diagnose cardiac diseases. To acquire the spatial signal characteristics from the thorax, multiple electrodes are commonly used. Displacements of electrodes affect the signal…
We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties…
We present a high-performance budgeted multi-level Monte Carlo method for estimates on the entire spatial domain of multi-PDE problems with random input data. The method is designed to operate optimally within memory and CPU-time…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity, such as wave re-entry caused by ischaemia. In terms of mathematical modelling, the…
We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that are modeled using the Richards' equation. We propose a stochastic extension for the empirical models that are…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
Meshfree methods for in silico modelling and simulation of cardiac electrophysiology are gaining more and more popularity. These methods do not require a mesh and are more suitable than the Finite Element Method (FEM) to simulate the…
The Markov chain Monte Carlo (MCMC) method is used to evaluate the imaginary-time path integral of a quantum oscillator with a potential that includes both a quadratic term and a quartic term whose coupling is varied by several orders of…
In this paper, we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the forward problem, we show that perfectly insulating regions (modeling ischemic regions in the cardiac tissue) can be…
We provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To…
Stochastic PDE eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic…
We study properties of the human electrocardiogram under the working hypothesis that fluctuations beyond the regular structure of single cardiac cycles are unpredictable. On this background we discuss the possibility to use the phase space…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…