Prediction of formation permeability is essential for safely storing
carbon dioxide in the subsurface. Traditional methods for predicting permeability are either very costly or
rely entirely on existing limited data, making them less accurate. To overcome these challenges, we
develop a workflow that combines physics-based simulations with machine learning. In this workflow we
train an artificial neural network which learns to predict reservoir permeability using only small number
of observed pressure measurements from underground wells. In this training process we keep a
differentiable flow simulator in the loop, which helps the model in improved learning by providing
feedback on the discrepancy of predicted and observed pressure. Our approach significantly outperform
conventional data driven methods, reducing prediction errors by more than 90%. Combining the speed and
flexibility of machine learning with the accuracy and reliability of physical simulations it provides a
powerful tool for better understanding of subsurface complex heterogeneity and helping ensure safe and
efficient CO2 storage operations.