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Efficient evaluation of small failure probability in high‐dimensional groundwater contaminant transport modeling via a two‐stage Monte Carlo method

In decision‐making for groundwater management and contamination remediation, it is important to accurately evaluate the probability of the occurrence of a failure event. For small failure probability analysis, a large number of model evaluations are needed in the Monte Carlo (MC) simulation, which is impractical for CPU‐demanding models. One approach to alleviate the computational cost caused by the model evaluations is to construct a computationally inexpensive surrogate model instead. However, using a surrogate approximation can cause an extra error in the failure probability analysis. Moreover, constructing accurate surrogates is challenging for high‐dimensional models, i.e., models containing many uncertain input parameters. To address these issues, we propose an efficient two‐stage MC approach for small failure probability analysis in high‐dimensional groundwater contaminant transport modeling. In the first stage, a low‐dimensional representation of the original high‐dimensional model is sought with Karhunen‐Loève expansion and sliced inverse regression jointly, which allows for the easy construction of a surrogate with polynomial chaos expansion. Then a surrogate‐based MC simulation is implemented. In the second stage, the small number of samples that are close to the failure boundary are re‐evaluated with the original model, which corrects the bias introduced by the surrogate approximation. The proposed approach is tested with a numerical case study and is shown to be 100 times faster than the traditional MC approach in achieving the same level of estimation accuracy.