Weighted Iterative Bayesian Compressive Sensing (WIBCS) for High Dimensional Polynomial Surrogate Construction


Surrogate construction has become a routine procedure when facing computationally intensive studies requiring multiple evaluations of complex models. In particular, surrogate models, otherwise called emulators or response surfaces, replace complex models in uncertainty quantification (UQ) studies, including uncertainty propagation (forward UQ) and parameter estimation (inverse UQ).

Further, surrogates based on Polynomial Chaos (PC) expansions are especially convenient for forward UQ and global sensitivity analysis, also known as variance-based decomposition. However, the PC surrogate construction strongly suffers from the curse of dimensionality. With a large number of input parameters, the number of model simulations required for accurate surrogate construction is prohibitively large. Relatedly, non-adaptive PC expansions typically include infeasibly large number of basis terms far exceeding the number of available model evaluations.

We develop Weighted Iterative Bayesian Compressive Sensing (WIBCS) algorithm for adaptive basis growth and PC surrogate construction leading to a sparse, high-dimensional PC surrogate with a very few model evaluations. The surrogate is then readily employed for global sensitivity analysis leading to further dimensionality reduction. Besides numerical tests, we demonstrate the construction on the example of Accelerated Climate Model for Energy (ACME) Land Model for several output QoIs at nearly 100 FLUXNET sites covering multiple plant functional types and climates, varying 65 input parameters over broad ranges of possible values.

This work is supported by the U.S. Department of Energy, Office of Science,
Biological and Environmental Research, Accelerated Climate Modeling for Energy (ACME) project.
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation,
a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National
Nuclear Security Administration under contract DE-AC04-94AL85000.

Dec 14, 2016
San Francisco, CA