Partial differential equations (PDEs) are ubiquitous throughout science, describing fundamental physical phenomena. We propose using machine learning to aid numerical PDE solvers with a predictor-corrector method. Starting from the initial condition, we iteratively predict the next timestep using a convolutional neural network (CNN), then correct” that prediction using an existing numerical method. The CNN structure lends itself well to grid-based methods, which include the majority of differential equation solvers. Advantages include amortizing the computational cost of training the neural network, which is expensive, over each evaluation, which is comparatively cheap. Moreover, this amortization process can be easily adapted to different classes of PDEs.

I’m participating in SuperUROP to learn the essentials of research in a systematic way. This research aligns with my background as I have prior research experience using neural nets as PDE solvers for turbulence equations. I hope to learn how to present and communicate my work effectively. I’m most excited to conduct novel research and learn more about this field!