Exciton-Polariton Condensates: A Fourier Neural Operator Approach

Advancements in semiconductor fabrication over the past decade have catalyzed extensive research into all-optical devices driven by exciton-polariton condensates. Preliminary validations of such devices, including transistors, have shown encouraging results even under ambient conditions. A significant challenge still remains for large scale application however: the lack of a robust solver that can be used to simulate complex nonlinear systems which require an extended period of time to stabilize. Addressing this need, we propose the application of a machine-learning-based Fourier Neural Operator approach to find the solution to the Gross-Pitaevskii equations coupled with extra exciton rate equations. This work marks the first direct application of Neural Operators to an exciton-polariton condensate system. Our findings show that the proposed method can predict final-state solutions to a high degree of accuracy almost 1000 times faster than CUDA-based GPU solvers. Moreover, this paves the way for potential all-optical chip design workflows by integrating experimental data.

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

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, given a set of controls, to a great deal of accuracy with only a fraction of the available information, while also reducing training times significantly compared to the original E2C and E2CO models.