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Uncertainty Quantification for Subsurface Flow and Transport: Coping With Nonlinearity/Irregularity via Polynomial Chaos Surrogate and Machine Learning

Subsurface flow and transport problems usually involve some degree of uncertainty. Polynomial chaos expansion can be used as surrogate of physical models for uncertainty quantification. However, a global model can hardly be found for model responses with strong nonlinearity or irregularity. In this study, we propose a novel approach by use of the classification method in machine learning, that is, supported vector machine, to cope with such nonlinearity/irregularity. Piecewise surrogate models are constructed in relatively smooth subdomains separated by the supported vector machine hyperplanes. We demonstrate the effectiveness of using the trained piecewise surrogate model in solute transport and two‐phase flow problems in homogeneous and heterogeneous porous media. The numerical results are compared with standard global polynomial chaos expansion results and the Monte Carlo benchmark. The proposed nonintrusive approach is able to accurately quantify uncertainty, with much smaller computational efforts.