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 to solve large-scale GCS problems with more affordable multi-fidelity training datasets. The Fourier Neural Operator 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.

翻译：基于深度学习的代理模型已被广泛应用于地质碳封存（GCS）问题中，以加速储层压力和CO2羽流迁移的预测。为了准确模拟该过程中涉及的复杂物理行为，需要大量来自物理数值模拟器的数据来训练模型。在实际应用中，由于大规模三维问题的高计算成本，可用的训练数据通常十分有限。因此，我们提出使用多保真度傅里叶神经算子，通过更经济的多保真度训练数据集来解决大规模GCS问题。傅里叶神经算子具有理想的网格不变性，这简化了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11万个网格单元的GCS储层模型上测试了模型效果。该多保真度模型能够以与使用相同数量高保真数据训练的高保真模型相当的精度进行预测，同时数据生成成本降低81%。我们进一步在具有更精细离散化（100万个网格单元）的同一储层模型上测试了多保真度模型的泛化能力。该案例中，高保真和低保真数据集由不同的地质统计模型和储层模拟器生成，使得问题更具挑战性。我们观察到，即使高保真数据极为有限，多保真度FNO模型仍能合理准确地预测压力场。