In a soup pot, you only need two thermometers to gauge the temperature everywhere — if you know heat travels in circles from the bottom. Science works the same way: from a handful of measurements, you want to reconstruct the full heat picture.
The system captures the gist of heat flow, compressing it into a handful of governing numbers. Like a chef who knows the soup's center is the hottest. Then, much like decomposing heat into waves, it learns to foresee the whole from these rules.
After training, the algorithm swiftly reconstructs the entire field from sparse data and gauges uncertainty using a confidence measure. Like a cook stirring with a ladle, sensing which parts are warmed through. Testing on a heat diffusion problem proved its precision. The real surprise: the system actually flags where its predictions might be off, a rare bit of self-critique for a machine.
Meteorologists do something similar: they condense millions of weather equations into a handful of dominant 'modes' to forecast rain or shine from sparse weather station data.