tanh(Ax+b) is simple, but the dataset it's supposed to work on is not easily summarised. I think that's the huge difference. The guys doing "sugar molecule" studies make progress by taking much simpler datasets, like random points.

Naiver-Stokes is much simpler because it operates by itself. Of course turbulence is hard but even there we usually care about its coarse features, we'd be content to throw away almost all the information provided the calculation of the wing's lift works out OK.