Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

• A practical multi-modal parameter estimation algorithm is proposed.
• The algorithm combines iterative stochastic ensemble method and k-means clustering.
• Truncated SVD is used for regularization of the output covariance matrix.
• K-means clustering forms sub-ensembles to explore disjoint parts of the search space.
• The algorithm is applied for parameter estimation of several subsurface flow models.

A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss–Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models.