Beyond that, the tips get less general-purpose. The two big over-arching ideas are:
1. Numerical code is the canonical example of "functional" code. If you prove all the pieces correct then the result is also correct. If you prove one wrong then you know why your overall code is wrong. As such, focusing more heavily than normal on proving each piece correct is prudent. Use automated techniques (like numerical gradient checking), and use randomized inputs. It's easier than you'd think for your favorite special cases to be correct in both right and wrong algorithms. Your eyes will deceive you, so use the computer to do your spot checks.
2. I lied in (1). Especially when you start involving GPUs, it's easy to have to start worrying about variable lifetimes, UAF, double-free, un-initialized memory, accidental clobberings, and other ways in which an innocent "functional" computation can stomp on something else you're doing. Still start with all the checks from (1), and if the parts are correct and the whole is broken then you're messing up global state somewhere. Tracking that down is more art than science, but one technique is adding a "poison" field, tracking deinit count, and otherwise exposing metrics regarding those failure modes. Panic/crash when you hit an invalid state, and once you figure out where the issue happens you can triage as normal (working backward from the broken state to figure out how you got there). With a solid memory management strategy up-front you'll not see this sort of thing, but if it's not something you've thought about then I wouldn't rule it out.
3. Not really another point, just an extension of (2), corruption can show up in subtle ways (like stack-copied pointers inside a paused async function closure which occasionally gets copied by your event loop). If global state is the issue, it's worth a full audit of the application.