A novel sampling-free algorithm for subsurface data assimilation using Gaussian process-derived sensitivities.

Area of Science:

• Hydrology
• Geosciences
• Computational Science

Background:

• Accurate hydraulic parameter characterization is crucial for subsurface flow and transport modeling.
• Ensemble-based methods are common but computationally intensive due to large ensemble requirements.
• Existing surrogate methods still suffer from sampling errors in sensitivity calculations.

Purpose of the Study:

• To develop a computationally efficient and accurate method for estimating subsurface hydraulic parameters.
• To introduce an adaptive Gaussian Process based Iterative Smoother (GPIS) algorithm.
• To analytically derive parameter sensitivity indices from a Gaussian Process (GP) surrogate.

Main Methods:

• An adaptive Gaussian Process based Iterative Smoother (GPIS) algorithm was developed.
• Parameter sensitivity indices were analytically derived from the GP surrogate.
• The GP surrogate was adaptively refined using updated parameter realizations.
• Numerical and experimental cases were used for testing and comparison with Iterative Ensemble Smoother (IES) and GP based Iterative Ensemble Smoother (GPIES).

Main Results:

• GPIS demonstrated superior estimation accuracy and computational efficiency compared to GPIES.
• Analytically derived GP sensitivities reduced sampling errors.
• The method effectively estimated heterogeneous hydraulic conductivity fields.

Conclusions:

• The proposed GPIS algorithm offers significant advantages for subsurface parameter estimation.
• GPIS provides a more accurate and computationally efficient alternative to existing ensemble-based and surrogate methods.
• The method has broad applicability in hydrological and other scientific modeling problems.