SciML
Dynamically Orthogonal (DO) Approximation
https://dspace.mit.edu/bitstream/handle/1721.1/120002/16m1095202.pdf?sequence=1&isAllowed=y
This paper focuses on the computational aspects of DO (a lot more approachable than the paper Chris linked which is very theoretical!). For me this was the best reference to understand DO: https://epubs.siam.org/doi/abs/10.1137/16M1109394
This paper focuses on doing DO on flow problems (I personally find the previous paper more approachable but perhaps this helps too): https://www.sciencedirect.com/science/article/pii/S0021999112005098
This paper is the conception of the DO equations and explains their derivation quite nicely: https://www.sciencedirect.com/science/article/pii/S0167278909002917
If you pursue this, I already have some preliminary work on DO methods that you can build on. And it would be great to contribute this to github.com/FHoltorf/LowRankIntegrators.jl
