Online learning to accelerate nonlinear PDE solvers: Applied to multiphase porous media flow
We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed method rely on four pillars: (i) dimensionless numbers as i...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
KeAi Communications Co. Ltd.
2025-12-01
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| Series: | Artificial Intelligence in Geosciences |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666544125000425 |
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| Summary: | We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed method rely on four pillars: (i) dimensionless numbers as input parameters for the machine learning model, (ii) simplified numerical model (two-dimensional) for the offline training, (iii) dynamic control of a nonlinear solver tuning parameter (numerical relaxation), (iv) and online learning for real-time improvement of the machine learning model. This strategy decreases the number of nonlinear iterations by dynamically modifying a single global parameter, the relaxation factor, and by adaptively learning the attributes of each numerical model on-the-run. Furthermore, this work performs a sensitivity study in the dimensionless parameters (machine learning features), assess the efficacy of various machine learning models, demonstrate a decrease in nonlinear iterations using our method in more intricate, realistic three-dimensional models, and fully couple a machine learning model into an open-source multiphase flow simulator achieving up to 85% reduction in computational time. |
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| ISSN: | 2666-5441 |