Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active
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ORIGINAL PAPER
Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces Daniel Erdal1,2
•
Sinan Xiao3 • Wolfgang Nowak3
•
Olaf A. Cirpka1
Accepted: 28 August 2020 Ó The Author(s) 2020
Abstract Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70–90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs. Keywords Global sensitivity analysis Sampling behavioral models Gaussian process emulation Stochastic engine
1 Introduction This work was supported by the Collaborative Research Center 1253 CAMPOS (Project 7: Stochastic Modeling Framework of Catchment-Scale Reactive Transport), funded by the German Research Foundation (DFG, Grant Agreement SFB 1253/1), the Sino-German (CSC-DAAD) Postdoc Scholarship Program 2018 (57395819) and Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy-EXC 2075-390740016. All own-developed codes necessary to run the Stochastic Engine used in this work are available via http://hdl.handle. net/10900.1/6a66361b-b713-4312-819b-18f82f27aa18.
Numerical modeling of environmental processes is an important tool for many researchers and practitioners. With the increasing availability of computer power, we also see an increase in the size and complexity of the modeled systems (e.g., Kollet et al. 2010). For example, to describe flow and transport in surface-
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