Abstract
A key challenge in reservoir management and other fields of engineering involves optimizing a nonlinear function iteratively. Due to the lack of available gradients in commercial reservoir simulators the attention over the last decades has been on gradient free methods or gradient approximations. In particular, the ensemble-based optimization has gained popularity over the last decade due to its simplicity and efficient implementation when considering an ensemble of reservoir models. Typically, a regression type gradient approximation is used in a backtracking or line search setting. This paper introduces an approximation of the Hessian utilizing a Monte Carlo approximation of the natural gradient with respect to the covariance matrix. This Hessian approximation can further be implemented in a trust region approach in order to improve the efficiency of the algorithm. The advantages of using such approximations are demonstrated by testing the proposed algorithm on the Rosenbrock function and on a synthetic reservoir field.
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The datasets generated during and/or analyzed during the current study are available from the corresponding authors on reasonable request.
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Acknowledgements
The authors acknowledge the Research Council of Norway and the industry partners, ConocoPhillips Skandinavia AS, Aker BP ASA, Vår Energi AS, Equinor ASA, Neptune Energy Norge AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS, and DEA Norge AS, of The National IOR Centre of Norway for support. The authors are also immensely grateful to Richard J. Robertson and Patrick N. Raanes for the comments on an earlier version of the manuscript.
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Zhang, Y., Stordal, A.S. & Lorentzen, R.J. A natural Hessian approximation for ensemble based optimization. Comput Geosci 27, 355–364 (2023). https://doi.org/10.1007/s10596-022-10185-z
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DOI: https://doi.org/10.1007/s10596-022-10185-z