Implicit-explicit and split-explicit super-time-stepping methods

What the math gives to ML

The paper develops a constructive multirate integration mechanism for additively split dynamics in which a stiff diffusion-like component is advanced by super-time-stepping while advection or learned drift remains explicit and local reactions can use localized implicit solves. The transferable asset is solve-decoupled coupling: many stable diffusion substeps can be inserted inside one macrostep without requiring a globally coupled implicit solve. This suggests neural ODE and diffusion-sampling architectures whose vector field is split into a known smoothing operator, a learned nonstiff drift, and an optional pointwise nonlinear term. The first useful test is whether the ExtSTS macrostep permits fewer score-network evaluations or larger stable solver steps at matched sample quality than Euler, Heun, and standard operator splitting.