Distributed Gauss-Newton Method for History Matching Problems with Multiple Best Matches

A novel assisted-history-matching (AHM) approach is developed to efficiently find multiple local minima of the objective function, by performing Gauss-Newton (GN) minimizations concurrently and and sharing information from dispersed regions in parameter space dynamically. To start, a large number of different initial parameter values (i.e., model realizations) are randomly generated and are used as base-cases for each realization. Production data for all realizations are obtained by simulating these base-cases concurrently. A local quadratic model around each base-case is constructed using the GN formulation, where the required sensitivity-matrix is approximated by linear interpolation of non-degenerated points that are closest to the given base-case. New search points are generated by minimizing the local quadratic approximate models. The base-cases are updated iteratively if their corresponding search points improve the data mismatch. Finally, each base case will converge to a local minimum in the vicinity of the initial base-case. The proposed approach is applied to different test problems. Most local minima of these test problems are found with satisfactory accuracy. Compared to traditional AHM approaches using derivative-free optimization algorithms using multiple initial start values, the propose approach may achieve a reduction factor in computer resource usage that is proportional to the number of parameters.