Flow Matching: Learning the Earth's Wind Patterns

I recently tackled an interesting challenge: predicting how wind moves across the Earth's surface using some clever math and machine learning. The core idea was pretty ambitious - teaching a neural network to figure out wind patterns just by knowing where air particles start and end up, without needing to track their exact paths in between. I built on Meta's flow matching approach, but applied it to a real-world problem using actual wind data from NOAA's weather forecasting system. The tricky part was handling the math of particle movement on a sphere (turns out the Earth being round makes things a bit more complicated!). I used a numerical method called RK4 to simulate these movements accurately and generate examples to train the model.