The global push for new energy solutions, such as Geothermal, and Carbon Capture and Sequestration initiatives has 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 conditions-aware Localized Learning method which extends the Embed-to-Control (E2C) and Embed-to-Control and Observed (E2CO) models to learn local representations of global state variables in an Advection-Diffusion Reaction system. We show that our model, trained on reservoir simulation data, is able to predict future states of the system for a given a 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.