The project’s goal is to radically enhance the simulation of flow through porous media application domain in order to boost forecasting capabilities to be able to increase oil recovery and production. The modeling of fluid dynamics in porous media will be addressed by focusing on improving learning mechanisms using different perspectives, from learning the form of differential equations from data to learning dynamical models with limited computing complexity.

 

Research challenges
Computational fluid dynamics has capitalized on machine learning with dimensionality reduction techniques for computing low rank modes and subspaces that characterize spatio-temporal data flows. This allowed reducing computational cost of simulations while enabling physically interpretable models. However, these methods suffer from limitations, e.g., they cannot capture transient behaviors or integrate multiple resolutions. Deep learning offers a new data driven approach to the modeling of dynamical systems underlying natural observations. This has recently given rise to a new and prolific research topic focused on exploiting deep learning methods for modeling spatio-temporal dynamics. 

 

This raises research challenges for machine learning and applied mathematics (or mechanics) communities such as:

• Learning from simulations and transfer learning. 
• Incorporating physical priors and learning with physical consistency. 
• Learning PDE constrained deep learning models for dynamical systems. 
• Optimization problem. 
• Modeling noise and uncertainties. 
• Learning dynamical models with limited computing complexity.