The interpolation using a single 4D RBF has been tested at an existing parameter point. The parameters are Teff, log(g), Z, and alpha elements. The result is as follows:

The processing time to make an RBF model: ~ 12 hours
The accuracy of a produced spectrum: 0.02 % (for a test sample)

Once the RBF model is generated, we can get an interpolated spectrum immediately. The accuracy is good enough.

I will check the accuracies at several parameter points as well.

The accuracies of this interpolation has been evaluated at 192 existing parameter points. An AMBRE original spectrum is removed when an interpolation is made there. The parameter points for this evaluation were selected to cover the whole grids. To save the processing time, the interpolations were made at 380-500nm, where the accuracies are expected to be worse than redder wavelengths. 

The RMS (%) is r.m.s of residuals between an AMBRE spectrum and a generated interpolation. The spectra are convolved with a quasi LSF (a Gaussian with 0.2 nm FWHM).  

Almost all the interpolations were generated in high accuracies (less than 1%), but 12% show >1% RMS. 1% show >10% RMS. I cannot any clear correlation of RMS to any parameters. When Teff and log(g) are fixed, at a specific metallicity interpolation spectra systematically show worse RMS. The reason on this and treatment for these low-accuracy interpolations are under discussion. 

RMS

RMS at Teff=7000 and log(g) = 4.0

We can close this ticket because we have developed the parameter interpolation and we have evaluated this method in PIPE2D-460. The code implementation should be done in PIPE2D-781.