A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater...

Area of Science:

• Environmental science
• Geosciences
• Computational modeling

Background:

• Groundwater flow models often involve complex, uncertain input fields like hydraulic conductivity.
• Accurate prediction of output fields (e.g., pressure head) is crucial for hydrological assessments.
• Existing methods may struggle with high-dimensional stochastic inputs and uncertainty quantification.

Purpose of the Study:

• To develop an efficient surrogate modeling approach for groundwater flow with stochastic inputs.
• To enable accurate prediction of output fields for unseen input scenarios.
• To establish a framework for forward uncertainty quantification in these models.

Main Methods:

• Utilized Karhunen-Loève expansion for log-normally distributed input fields.
• Applied manifold learning (local tangent space alignment) for Gaussian process Bayesian inference.
• Employed Hamiltonian Monte Carlo and Monte Carlo methods for sampling and analysis.

Main Results:

• Developed a surrogate model capable of capturing output fields from stochastic inputs.
• Successfully performed Gaussian process Bayesian inference in an abstract feature space.
• Demonstrated the approach's accuracy on 2-D Darcy flow and 3-D Richards equation models.

Conclusions:

• The proposed surrogate modeling approach accurately predicts groundwater flow outputs under uncertainty.
• The framework provides a robust method for forward uncertainty quantification in hydrological modeling.
• This technique offers a computationally efficient way to handle complex stochastic problems in geosciences.