Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo
Abstract
Mathematical models in biology involve many parameters that are uncertain or in some cases unknown. Over the last years, increased computing power has expanded the complexity and increased the number of degrees of freedom of many such models. For this reason, efficient uncertainty quantification algorithms are now needed to explore the often large parameter space of a given model. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have become very popular in the mathematical, engineering, and financial literature for the quantification of uncertainty in model predictions. However, applying these methods to physiologically relevant simulations is a difficult task given the typical complexity of the models and geometries involved. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convectiondiffusion model for tracer transport within the brain. We show that QMC outperforms standard Monte Carlo simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard Monte Carlo methods and should therefore be preferred for brain transport models.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.02311
 Bibcode:
 2020arXiv200302311C
 Keywords:

 Computer Science  Computational Engineering;
 Finance;
 and Science;
 Mathematics  Numerical Analysis;
 Statistics  Computation
 EPrint:
 Key words: Multilevel Monte Carlo, quasi Monte Carlo, brain simulation, brain fluids, finite element method, biomedical computing, random fields, diffusionconvection