Bayesian Compressive Sensing Framework for High-Dimensional Surrogate Model Construction


Naive Monte-Carlo approaches are ineffective for computationally intensive studies of complex physical models as they require prohibitively many sampled simulations for reasonable accuracy.
In this work, we build computationally inexpensive surrogate model in order to accelerate both forward (e.g., uncertainty propagation and sensitivity analysis) and inverse (e.g., calibration) UQ methods. We apply Polynomial Chaos (PC) spectral expansions to build surrogate relationships between output quantities and model parameters using as few forward model simulations as possible. For a complex model with a large number of input parameters, building a PC surrogate model is challenged by high dimensionality: there is typically insufficient model simulation data as well
as a prohibitively large number of spectral basis terms. Bayesian compressive sensing (BCS) approach [Babacan et al., 2010] is employed in order to detect a sparse polynomial basis set that best captures
the model outputs. We enhance the BCS algorithm with adaptive basis reweighing and basis growth.
Besides proof-of-concept studies for synthetic models, we demonstrate the iterative BCS method on the Community Land Model with about 80 input parameters, and obtain global sensitivity information for 5 outputs with respect to all input parameters using less than 10000 model simulations - a very small number for an 80-dimensional input parameter space [Sargsyan et al., 2014].

Jun 27, 2014
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM
Salt Lake City, UT