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Theoretical and Practical Aspects of Stein Variational Gradient Descent with Applications to Data Assimilation
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, Petroleum Geostatistics 2019, Sep 2019, Volume 2019, p.1 - 5
Abstract
We have introduced and applied the Stein variational gradient descent (SVGD) algorithm to the reservoir history matching problem. The method has been extended with a Monte Carlo approximation of the gradient of the measurement function using the reproducible property of the reproducing kernel Hilbert space in order to avoid adjoint implementation. Furthermore we have implemented SVGD with p-kernels in order to extend the applicability to higher dimension than the standard Gaussian kernels used in the literature. The gradient approximation was validated both theoretically and on a toy model. Implementation on larger problems will be addressed in the future. We also showed using a reservoir model that the SVGD with p-kernels provided better estimates of the uncertainty than the standard Gaussian kernels. Further comparison with ensemble-based methods and other gradient-based methods is left for future research.