Surrogate models are useful tools for enabling uncertainty quantification (UQ) tasks that rely on performing many expensive model evaluations, as surrogate modeling looks to replace 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 that the approximation accuracy of Kriging surrogate models can be significantly improved when polynomial chaos expansions are used to describe the trend of Kriging. A basis-adaptive least-angle-regression strategy is shown to be particularly useful for inducing sparsity in polynomial chaos expansions to handle 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.

代理模型是用于执行依赖于执行许多昂贵的模型评估的不确定性量化（UQ）任务的有用工具，因为代理建模希望用便宜的评估代理代替昂贵的高保真模型。本文研究了稀疏多项式混沌和Kriging方法来替代具有参数和初始条件的概率不确定性的第一性原理模型的替代模型。在具有20个不确定参数的布洛芬分批冷却结晶的二维总体平衡（2D-PB）模型上证明了替代建模方法。我们的分析表明，不仅稀疏多项式混沌展开对于概率UQ而言是强大的，而且，当使用多项式混沌展开来描述Kriging趋势时，可以大大提高Kriging替代模型的近似精度。一种基本的最小角度回归策略对于在多项式混沌扩展中引入稀疏性来处理具有相对大量不确定输入的问题特别有用。举例说明了稀疏多项式基于混沌和Kriging的替代模型对各种正向和反向UQ问题的实用性，包括全局灵敏度分析以及2D-PB模型的贝叶斯和最大后验参数估计，从而大大节省了计算成本（高达30,000倍）。一种基本的最小角度回归策略对于在多项式混沌扩展中引入稀疏性来处理具有相对大量不确定输入的问题特别有用。举例说明了稀疏多项式基于混沌和Kriging的替代模型对各种正向和反向UQ问题的实用性，包括全局灵敏度分析以及2D-PB模型的贝叶斯和最大后验参数估计，从而大大节省了计算成本（高达30,000倍）。一种基本的最小角度回归策略对于在多项式混沌扩展中引入稀疏性来处理具有相对大量不确定输入的问题特别有用。举例说明了稀疏多项式基于混沌和Kriging的替代模型对各种正向和反向UQ问题的实用性，包括全局灵敏度分析以及2D-PB模型的贝叶斯和最大后验参数估计，从而大大节省了计算成本（高达30,000倍）。