Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology
Additional information
Authors
Type
Journal Article
Language
English
Abstract
We present a novel approach aimed at high-performance uncertainty quantification for time-dependent problems governed by partial differential equations. In particular, we consider input uncertainties described by a Karhunen-Loève expansion and compute statistics of high-dimensional quantities-of-interest, such as the cardiac activation potential. Our methodology relies on a close integration of multilevel Monte Carlo methods, parallel iterative solvers, and a space-time discretization. This combination allows for space-time adaptivity, time-changing domains, and to take advantage of past samples to initialize the space-time solution. The resulting sequence of problems is distributed using a multilevel parallelization strategy, allocating batches of samples having different sizes to a different number of processors. We assess the performance of the proposed framework by showing in detail its application to the solution of nonlinear equations arising from cardiac electrophysiology. Specifically, we study the effect of spatially-correlated perturbations of the heart fibers' conductivities on the mean and variance of the resulting activation map. As shown by the experiments, the theoretical rates of convergence of multilevel Monte Carlo are achieved. Moreover, the total computational work for a prescribed accuracy is reduced by an order of magnitude with respect to standard Monte Carlo methods.
Keywords
Uncertainty quantification, Multilevel methods, Space-time finite elements (3D+1), Cardiac electrophysiology, Monodomain equation
Journal
Journal of computational physics
Volume
433
Number ( Month )
May
Pages (or article number)
110164
Diffusion
License
CC BY-NC-ND
Visibility
Public
Status open access
Hybrid
