Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical simulators are required to train a model to accurately predict the complex physical behaviors associated with this process. In practice, the available training data are always limited in large-scale 3D problems due to the high computational cost. Therefore, we propose to use a multi-fidelity Fourier neural operator (FNO) to solve large-scale GCS problems with more affordable multi-fidelity training datasets. FNO has a desirable grid-invariant property, which simplifies the transfer learning procedure between datasets with different discretization. We first test the model efficacy on a GCS reservoir model being discretized into 110k grid cells. The multi-fidelity model can predict with accuracy comparable to a high-fidelity model trained with the same amount of high-fidelity data with 81% less data generation costs. We further test the generalizability of the multi-fidelity model on a same reservoir model with a finer discretization of 1 million grid cells. This case was made more challenging by employing high-fidelity and low-fidelity datasets generated by different geostatistical models and reservoir simulators. We observe that the multi-fidelity FNO model can predict pressure fields with reasonable accuracy even when the high-fidelity data are extremely limited. The findings of this study can help for better understanding of the transferability of multi-fidelity deep learning surrogate models.

翻译：基于深度学习的替代模型已广泛应用于地质碳封存（GCS）问题中，以加速储层压力和CO₂羽流运移的预测。要训练模型精确预测这一过程中涉及的复杂物理行为，需要大量来自基于物理的数值模拟器的数据。然而在实际应用中，由于大规模三维问题的计算成本高昂，可获取的训练数据往往十分有限。为此，我们提出采用多保真度傅里叶神经算子（FNO）结合更经济的多保真度训练数据集来解决大规模GCS问题。FNO具有理想的网格不变特性，可简化不同离散化数据集之间的迁移学习过程。我们首先在离散化为110k网格单元的GCS储层模型上测试了模型有效性：该多保真度模型在数据生成成本降低81%的条件下，能达到与使用相同数量高保真数据训练的高保真模型相当的预测精度。进一步地，我们在相同储层模型但采用100万网格单元的更精细离散化方案上测试了多保真度模型的泛化能力。通过采用不同地质统计学模型和储层模拟器生成的高保真度与低保真度数据集，该案例更具挑战性。实验表明，即使在高保真数据极其有限的情况下，多保真度FNO模型仍能合理预测压力场。本研究有助于深入理解多保真度深度学习替代模型的可迁移性。