This study investigates the integration of machine learning (ML) and data assimilation (DA) techniques, focusing on implementing surrogate models for Geological Carbon Storage (GCS) projects while maintaining high fidelity physical results in posterior states. Initially, we evaluate the surrogate modeling capability of two distinct machine learning models, Fourier Neural Operators (FNOs) and Transformer UNet (T-UNet), in the context of CO$_2$ injection simulations within channelized reservoirs. We introduce the Surrogate-based hybrid ESMDA (SH-ESMDA), an adaptation of the traditional Ensemble Smoother with Multiple Data Assimilation (ESMDA). This method uses FNOs and T-UNet as surrogate models and has the potential to make the standard ESMDA process at least 50% faster or more, depending on the number of assimilation steps. Additionally, we introduce Surrogate-based Hybrid RML (SH-RML), a variational data assimilation approach that relies on the randomized maximum likelihood (RML) where both the FNO and the T-UNet enable the computation of gradients for the optimization of the objective function, and a high-fidelity model is employed for the computation of the posterior states. Our comparative analyses show that SH-RML offers better uncertainty quantification compared to conventional ESMDA for the case study.

研究使用机器学习和数据同化技术，利用替代模型对地质碳储存项目进行集成，并在保持高保真度的情况下得到后验状态的结果。结果表明，利用机器学习模型进行数据同化可以显著提高标准ESMDA过程的速度，并且使用替代模型实现的随机最大似然方法在确定性建模和不确定性量化方面优于传统的ESMDA方法。

人工智能增强的数据同化与不确定性量化在地质碳储存中的应用