Surrogate modeling for fast uncertainty quantification: Application to 2D population balance models

Abstract

Surrogate modeling is a useful tool for enabling uncertainty quantification (UQ) tasks that require many expensive model evaluations, as it replaces expensive high-fidelity models with cheap-to-evaluate surrogates. This paper investigates sparse polynomial chaos and Kriging methods for surrogate modeling of first-principles models with probabilistic uncertainty in parameters and initial conditions. The surrogate modeling methods are demonstrated on a 2-dimensional population balance (2D-PB) model for batch cooling crystallization of ibuprofen with 20 uncertain parameters. Our analysis indicates that not only sparse polynomial chaos expansions are powerful for probabilistic UQ, but also the approximation accuracy of Kriging surrogate models can be significantly improved when polynomial chaos expansions are used to describe their trend. A basis-adaptive least-angle-regression strategy is shown to be particularly useful for inducing sparsity in polynomial chaos expansions, allowing for dealing with problems with a relatively large number of uncertain inputs. The utility of sparse polynomial chaos- and Kriging-based surrogate models is illustrated for various forward and inverse UQ problems, including global sensitivity analysis as well as Bayesian and maximum a posteriori parameter estimation of the 2D-PB model, where massive savings in computational cost (up to 30,000-fold) are observed.