Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2 plume predictions near, and far away, from the monitoring wells.

翻译：针对地质碳封存监测中的多物理场反问题，当多模态时移数据采集成本高昂且数值模拟计算代价巨大时，求解尤为困难。我们通过结合计算成本低廉的学习型替代模型与学习型约束来克服这些挑战。这种结合不仅显著改进了关键流体流动属性——渗透率的反演精度，还为多模态数据（包括井中测量数据与主动源时移地震数据）的反演提供了天然平台。通过引入学习型约束，我们提出了一种计算可行且保持高精度的反演方法。该方法通过训练深度神经网络（即正则化流）实现，该网络迫使模型迭代始终保持在数据分布内，从而保障了作为计算密集型多相流模拟（涉及偏微分方程求解）替代模型的傅里叶神经算子精度。通过围绕地质碳封存问题精心设计的系列实验，我们在两种不同数据模态（时移井数据与时移地震数据）上验证了所提出约束优化方法的有效性。尽管两种模态的渗透率反演各有优劣，但联合反演融合了两者优势，在监测井近场与远场均能获得更优的渗透率反演结果与CO2羽流预测。