Matteo Croci
Basque Center for Applied Mathematics (BCAM) – 🇪🇸 Bilbao (Spain)
Forward UQ in brain simulation: from multilevel Monte Carlo to MLBLUEs
The brain fluid and solute clearance dynamics play a key role in the onset and progression of neurodegenerative disorders such as Alzheimer’s disease. However, the mechanisms behind these phenomena are still poorly understood. Numerical algorithms offer a faster, cheaper, and more ethical alternative to human experimentation while providing data that may otherwise be unobtainable. However, the numerical modeling of the brain is computationally expensive and the data available is affected by a large degree of uncertainty. As a consequence, uncertainty quantification (UQ) plays a crucial role in this field.
This talk is divided in two parts:
- Application: Forward UQ in brain simulation.
We select multiple leading hypotheses on brain solute movement and, for each of these, we construct corresponding partial differential equation models in which the uncertainty in the physical parameters is modelled via random fields. Then, we leverage multilevel Monte Carlo methods to estimate the statistical properties of model predictions and consequently isolate the most likely hypotheses. We show that multilevel Monte Carlo can reduce the computational cost of the estimation from tens of years to a couple of weeks.
- Methodology: Multi-output multilevel best linear unbiased estimators (MLBLUE).
While efficient, multilevel Monte Carlo is still too expensive for brain UQ. In the second part of the talk we show how to accelerate Monte Carlo estimation by leveraging a new class of methods for multi-output multilevel/multifidelity estimation. These methods, called MLBLUEs, are both provenly optimal and come with an in-built automatic model selection and sample allocation strategy. This means that MLBLUEs can leverage any set of correlated computational models (e.g. different grids, equations, dimensions, physics, surrogate and reduced-order models) and yield the best possible Monte Carlo estimator that can be constructed from this set. We demonstrate the efficacy of the new methods in practical UQ problems with model heterogeneity.