Physics-Informed Localized Learning for Advection-Diffusion-Reaction Systems

The global push to advance Carbon Capture and Sequestration initiatives and green energy solutions, such as geothermal, have thrust new demands upon the current state-of-the-art subsurface fluid simulators. The requirement to be able to simulate a large order of reservoir states simultaneously, in a short period of time, has opened the door of opportunity for the application of machine learning techniques for surrogate modelling. We propose a novel physics-informed and boundary condition-aware Localized Learning method which extends the Embed-to-Control (E2C) and Embed-to-Control and Observe (E2CO) models to learn local representations of global state variables in an Advection-Diffusion Reaction system. Trained on reservoir simulation data, we show that our model is able to predict future states of the system, for a given set of controls, to a great deal of accuracy with only a fraction of the available information. It hence reduces training times significantly compared to the original E2C and E2CO models, lending to its benefit in application to optimal control problems.