Data-driven uncertainty quantification for predictive flow and transport modeling using support vector machines

• Published in: Computational geosciences Vol. 23; no. 4; pp. 631 - 645
• Main Authors: He, Jiachuan, Mattis, Steven A., Butler, Troy D., Dawson, Clint N.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.08.2019; Springer Nature B.V; Springer
• Subjects: Computer applications; Computer Science; Computer simulation; Contaminants; Data; Earth and Environmental Science; Earth Sciences; Frameworks; Geology; Geotechnical Engineering & Applied Earth Sciences; Groundwater; Groundwater flow; Hydrogeology; Inverse problems; Mathematical Modeling and Industrial Mathematics; Mathematical models; Modelling; Original Paper; Parameter uncertainty; Predictions; Probability theory; Soil Science & Conservation; Solutions; Spatial distribution; Statistical analysis; Statistical methods; Support vector machines; Transport; Transport equations; Measure theory; Support vector regression; Parameter estimation; Hydraulic conductivity; Stochastic inverse problems
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-018-9762-4

Specification of hydraulic conductivity as a model parameter in groundwater flow and transport equations is an essential step in predictive simulations. It is often infeasible in practice to characterize this model parameter at all points in space due to complex hydrogeological environments leading to significant parameter uncertainties. Quantifying these uncertainties requires the formulation and solution of an inverse problem using data corresponding to observable model responses. Several types of inverse problems may be formulated under various physical and statistical assumptions on the model parameters, model response, and the data. Solutions to most types of inverse problems require large numbers of model evaluations. In this study, we incorporate the use of surrogate models based on support vector machines to increase the number of samples used in approximating a solution to an inverse problem at a relatively low computational cost. To test the global capabilities of this type of surrogate model for quantifying uncertainties, we use a framework rooted in measure theory for constructing pullback and push-forward probability measures to study the data-to-parameter-to-prediction propagation of uncertainties under minimal statistical assumptions. Additionally, we demonstrate that it is possible to build a support vector machine using relatively low-dimensional representations of the hydraulic conductivity to propagate distributions. The numerical examples further demonstrate that we can make reliable probabilistic predictions of contaminant concentration at spatial locations.