- Half "hard maths" algorithms. i.e. cominbatorics, geometry, etc.
- Half "fuzzy maths" algorithms. i.e. heuristics, approximation, machine learning.
The idea being to solve the parts that can be easily solved by hard maths with those hard maths so that you can reduce the problem space for when you apply the fuzzy maths to solve the rest of the problem.
In other words, it's taking the problem, breaking out discrete pieces to solve with well established hard maths, using heuristics & numerical solutions to tackle the remaining known problems without "easy" analytical solutions, then using ML to fill in all the gaps and glue the whole thing together.
The article gives a concrete example in the same paragraph: "For example, AI algorithms could get close to a solution quickly and efficiently, and then the gap between the AI answer and the true solution can be filled by high-precision computing."
Interestingly the example is backwards (statistical reasoning first, hard reasoning second) compared to traditional usage of "hybrid" in AI and control contexts.
From the article it looks like half AI guessing the solution, half some static algorithm fixing the result to be better. Not sure how it's supposed to really work.
one variant of this is sciml approaches where you use an ODE solver wrapped around a NN. the ODE solver guarantees you get the right conversation laws which NNs don't do well and the NN is more accurate than the hand written model since it doesn't ignore the higher order effects.
Half algorithm & half user manual?
Half algorithm & half class?