Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo
Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty—from uncertain input parameters to uncertain output quantities—in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Wiley
2020
|
| _version_ | 1797059209450225664 |
|---|---|
| author | Croci, M Vinje, V Rognes, ME |
| author_facet | Croci, M Vinje, V Rognes, ME |
| author_sort | Croci, M |
| collection | OXFORD |
| description | Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty—from uncertain input parameters to uncertain output quantities—in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon standard Monte Carlo (MC) methods, but their applicability and performance in biomedical applications is underexplored. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convection‐diffusion model of tracer transport within the brain. We show that QMC outperforms standard MC simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard MC methods and should therefore be preferred for brain transport models. |
| first_indexed | 2024-03-06T20:00:57Z |
| format | Journal article |
| id | oxford-uuid:27457012-a41f-49ad-a2d8-90fcaa300e06 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:00:57Z |
| publishDate | 2020 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:27457012-a41f-49ad-a2d8-90fcaa300e062022-03-26T12:06:04ZFast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte CarloJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:27457012-a41f-49ad-a2d8-90fcaa300e06EnglishSymplectic ElementsWiley2020Croci, MVinje, VRognes, MEEfficient uncertainty quantification algorithms are key to understand the propagation of uncertainty—from uncertain input parameters to uncertain output quantities—in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon standard Monte Carlo (MC) methods, but their applicability and performance in biomedical applications is underexplored. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convection‐diffusion model of tracer transport within the brain. We show that QMC outperforms standard MC simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard MC methods and should therefore be preferred for brain transport models. |
| spellingShingle | Croci, M Vinje, V Rognes, ME Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo |
| title | Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo |
| title_full | Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo |
| title_fullStr | Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo |
| title_full_unstemmed | Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo |
| title_short | Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo |
| title_sort | fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi monte carlo |
| work_keys_str_mv | AT crocim fastuncertaintyquantificationoftracerdistributioninthebraininterstitialfluidwithmultilevelandquasimontecarlo AT vinjev fastuncertaintyquantificationoftracerdistributioninthebraininterstitialfluidwithmultilevelandquasimontecarlo AT rognesme fastuncertaintyquantificationoftracerdistributioninthebraininterstitialfluidwithmultilevelandquasimontecarlo |