Slightly different approach that I should have tried long ago for the ENSO model. Instead of training on the time-series, train on the complex Fourier series in frequency space.

So, this is trained on intervals of the ENSO SOI spectrum (in yellow), and it fills in the rest of the spectrum. Even though there are only 3 known lunar periods + 1 solar, because of the nonlinear Navier-Stokes doubling with multiple interactions due to the precision required of the orbits, it generates a very busy spectral waveform (much more variable than a conventional tidal spectrum)


In real space, the inverse fit captures the time-series with a high >0.8 correlation coefficient.