Lessons Learned

📜 This project focused on developing ML based time-integration schemes that could be applied on the 2D Rayleigh-Benard convection problem. The main idea was to build a Fourier Neural Operator based model that would approximate

$$ U(t+\Delta t) \simeq ML\left(U(t)\right) $$

where $U(t)$ represent the input field (velocity, buoyancy, pressure) at a given time on the full 2D grid, and $U(t+\Delta t)$ is the output field after a given time-step $\Delta t$, chosen to be fixed for one given model.

The model is supposed to be used in combination of Spectral Deferred Corrections (SDC) to predict an initial guess at several time point within a time-step, corrected later by the SDC iterations to produce an accurate solution.

Here is a summary of some of the main lessons learned while trying to build such ML models ...

1. Learning the update rather than the solution
2. Transformation seems to not matter, as long as it's global
3. Up-scaling helps more than increasing the number of Fourier layers