Right now, we have two different approaches for emulation.
The standard one, predicting the $C_\ell$'s on a multipole grid with all integer multipoles
Emulation the Chebyshev coefficients and using them to interpolate on the required grid
The latter has several advantages, but is also prone to numerical instability.
The best thing is to make something intermediate:
Emulates the $C\ell$'s on the Chebyshev nodes grid, between the chosen $\ell\mathrm{min}-\ell_\mathrm{max}$
Evaluates the Chebyshev coefficients $a_{\ell m}$
Interpolates as in the previous scenario
This will also requires adequate AD rules (in a subsequent task).
Right now, we have two different approaches for emulation.
This will also requires adequate AD rules (in a subsequent task).