I have a 40-variable optimisation problem that seems to have a lot of local minima.  One of the simplest ways to explore them was to drop a load of optimisations from different starting points and run them downhill, which is what you see in the video below.  Vertical is error score (in this case, the degree of mismatch of some particle beams), and horizontal is radius of the parameter vector away from the origin (in this case, related to magnet power consumption).  I'm using radius because I don't have 40 horizontal axes for each dimension, but you can see some features already, with points on the bottom left being particularly good, and there's a radius beyond which things get worse again.   #optimisation #physics <p><video src='posts/202605/post-20260507-191625-a.mp4' loading='lazy' preload='metadata' controls></video></p>