How chaotic is chaos? How some AI for Science / SciML papers are overstating accuracy claims

Just how chaotic are chaotic systems? Many of you may have heard of “the butterfly effect” but don’t quite know the mathematics behind such systems. What I want to demonstrate is the “sensitive dependence to initial conditions” property of chaotic systems and just how sensitive these systems are. The reason this has come up is that I have seen some AI papers claiming to be able to predict the…