Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these researchers are Marcolli, Connes, Kreimer (also working on the Hopf algebra approach) and Konsani. You can read about Marcolli's work here, and about the joint work by Connes and Marcolli here.
Now, in the wikipedia article on the Navier-Stokes Equations, there is a short paragraph on Wyld Diagrams. It is stated there that they are similar to the Feynman diagrams studied in QFT. Since motives and other algebraic approaches are currently used to study these Feynman Diagrams, I was wondering if these approaches could also aid in studying the Wyld Diagrams, and therefore indirectly the Navier-Stokes equations.
If so, how? If not, why not?
Please note that I'm far from an expert in any of these fields, and that I have asked a similar question on the theoretical physics SE website.
Thanks in advance.