Enhancing data assimilation and uncertainty quantification: machine learning for better covariance estimation

Vinicius Luiz Santos Silva, Gabriel Serrao Seabra, Alexandre Anoze Emerick

Keywords: ensemble data assimilation, inverse problem, localization, reservoir simulation, machine learning, covariance estimation

Abstract: Ensemble-based data assimilation is a powerful tools for updating geological reservoir models using dynamic data, with applications in hydrocarbon production, groundwater management, carbon storage, and geothermal energy. However, small ensemble sizes —due to the high computational cost of simulations— can introduce sampling errors and spurious correlations, leading to poor covariance estimations and degraded uncertainty quantification. Localization techniques help mitigate these effects by tapering updates based on the distance between observations and model parameters. Nonetheless, for cases lacking spatial relationships, distance-based localization is ineffective. To overcome these limitations, we propose a novel distance-free localization strategy using machine learning models tailored for tabular data. Additionally, we introduce a simple correction to the prior cross-covariance to improve localization in low-dimensional problems. Integrated into the Ensemble Smoother with Multiple Data Assimilation (ES-MDA), our methods were tested on scalar and grid-based parameters. Results show improved cross-covariance estimates and enhanced data assimilation performance for all cases (with/without spatial relationships), preserving ensemble variance while maintaining data match quality.

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Submission Number: 35