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Table 4

Cross-validation tests for the active-regions component of the model trained on Sun RV and various activity indicators.

Active regions Magnetic cycle kernel Cross-validation score RMS (m/s)
Indicators Model Modes Kernel Train set Test set
FWHM + BIS data-driven 1 M3/2 M1/2 –205.74 (−208.25−2.73+2.48)$\left( { - 208.25_{ - 2.73}^{ + 2.48}} \right)$ 0.54 ± 0.03 0.88 ± 0.02
FWHM + BIS data-driven 2 M1/2 M1/2 –206.15 (−208.68−2.72+2.39)$\left( { - 208.68_{ - 2.72}^{ + 2.39}} \right)$ 0.58 ± 0.02 0.88 ± 0.02
 phot +BIS+logRHK′${\rm{phot}} + {\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M3/2 M1/2 –206.80 (−210.93−3.55+3.27)$\left( { - 210.93_{ - 3.55}^{ + 3.27}} \right)$ 0.62 ± 0.02 0.87 ± 0.02
FWHM + BIS data-driven 2 M3/2 M1/2 –206.85 (−209.47−2.77+2.45)$\left( { - 209.47_{ - 2.77}^{ + 2.45}} \right)$ 0.62 ± 0.02 0.87 ± 0.02
 phot + FWHM + BIS +logRHK′${\rm{phot}} + {\rm{FWHM}} + {\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M3/2 M1/2 –207.36 (−212.00−3.88+3.52)$\left( { - 212.00_{ - 3.88}^{ + 3.52}} \right)$ 0.62 ± 0.02 0.88 ± 0.02
FWHM + BIS data-driven 1 M3/2 M3/2 –207.68 ( −211.03−4.45+3.17)$( - 211.03_{ - 4.45}^{ + 3.17})$ 0.54 ± 0.02 0.92 ± 0.03
 phot +BIS+logRHK′${\rm{phot}} + {\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M1/2 M3/2 –207.70 (−212.03−3.70+3.19)$\left( { - 212.03_{ - 3.70}^{ + 3.19}} \right)$ 0.59 ± 0.02 0.88 ± 0.02
phot + FWHM + BIS data-driven 2 M3/2 M1/2 –208.20 (−212.39−3.63+3.28)$\left( { - 212.39_{ - 3.63}^{ + 3.28}} \right)$ 0.62 ± 0.02 0.88 ± 0.02
 phot +BIS+logRHK′${\rm{phot}} + {\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M1/2 M1/2 –208.45 (−212.45−3.27+3.22)$\left( { - 212.45_{ - 3.27}^{ + 3.22}} \right)$ 0.61 ± 0.02 0.88 ± 0.02
 phot + BIS +logRHK′${\rm{phot}} + {\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M3/2 M3/2 –208.47 (−213.65−4.02+3.59)$\left( { - 213.65_{ - 4.02}^{ + 3.59}} \right)$ 0.64 ± 0.02 0.89 ± 0.02
phot + BIS data-driven 2 M1/2 M1/2 –208.62 (−211.57−2.95+2.65)$\left( { - 211.57_{ - 2.95}^{ + 2.65}} \right)$ 0.59 ± 0.02 0.88 ± 0.02
 FWHM + BIS + logRHK′${\rm{FWHM + BIS + }}\log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M3/2 M1/2 –208.65 (−212.20−3.33+2.88)$\left( { - 212.20_{ - 3.33}^{ + 2.88}} \right)$ 0.62 ± 0.02 0.89 ± 0.02
phot + BIS data-driven 2 M3/2 M1/2 –208.96 (−212.57−3.45+2.94)$\left( { - 212.57_{ - 3.45}^{ + 2.94}} \right)$ 0.61 ± 0.02 0.89 ± 0.02
 phot + FWHM + BIS +logRHK′${\rm{phot}} + {\rm{FWHM}} + {\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M1/2 M1/2 –209.05 (−214.42−4.02+3.79)$\left( { - 214.42_{ - 4.02}^{ + 3.79}} \right)$ 0.61 ± 0.03 0.89 ± 0.02
BIS+logRHK′${\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M1/2 M1/2 –209.41 (−212.92−3.64+3.10)$\left( { - 212.92_{ - 3.64}^{ + 3.10}} \right)$ 0.62 ± 0.02 0.90 ± 0.02
FWHM + BIS data-driven 2 M1/2 M3/2 –209.47 (−213.30−3.14+2.95)$\left( { - 213.30_{ - 3.14}^{ + 2.95}} \right)$ 0.60 ± 0.03 0.90 ± 0.02
phot + FWHM + BIS data-driven 2 M1/2 M1/2 –209.68 (−213.38−3.40+2.96)$\left( { - 213.38_{ - 3.40}^{ + 2.96}} \right)$ 0.60 ± 0.02 0.88 ± 0.02
 phot + FWHM + BIS + logRHK′${\rm{phot + FWHM + BIS + }}\log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M1/2 M3/2 –209.72 (−215.17−4.09+3.76)$\left( { - 215.17_{ - 4.09}^{ + 3.76}} \right)$ 0.61 ± 0.03 0.90 ± 0.02
FWHM + BIS data-driven 1 M1/2 M1/2 –209.80 (−213.66−3.28+3.14)$\left( { - 213.66_{ - 3.28}^{ + 3.14}} \right)$ 0.62 ± 0.03 0.87 ± 0.02
 FWHM + BIS + logRHK′${\rm{FWHM + BIS + }}\log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M1/2 M1/2 –209.87 (−213.57−3.41+2.96)$\left( { - 213.57_{ - 3.41}^{ + 2.96}} \right)$ 0.60 ± 0.02 0.90 ± 0.02
BIS data-driven 2 M1/2 M1/2 –209.95 (−213.33−3.42+2.93)$\left( { - 213.33_{ - 3.42}^{ + 2.93}} \right)$ 0.60 ± 0.03 0.90 ± 0.02
BIS data-driven 2 M1/2 M3/2 –210.43 (−213.91−3.38+3.08)$\left( { - 213.91_{ - 3.38}^{ + 3.08}} \right)$ 0.60 ± 0.03 0.91 ± 0.02
FWHM + BIS data-driven 2 M3/2 M3/2 –210.82 (−214.73−3.27+2.98)$\left( { - 214.73_{ - 3.27}^{ + 2.98}} \right)$ 0.65 ± 0.02 0.90 ± 0.02
 phot +FWHM+BIS+logRHK′${\rm{phot}} + {\rm{FWHM}} + {\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M3/2 M3/2 –211.06 (−216.91−3.72+3.64)$\left( { - 216.91_{ - 3.72}^{ + 3.64}} \right)$ 0.62 ± 0.02 0.92 ± 0.02
phot + BIS data-driven 2 M1/2 M3/2 –211.40 (−214.57−3.00+2.65)$\left( { - 214.57_{ - 3.00}^{ + 2.65}} \right)$ 0.61 ± 0.02 0.90 ± 0.02
BIS data-driven 2 M3/2 M1/2 –211.43 (−214.91−3.48+3.06)$\left( { - 214.91_{ - 3.48}^{ + 3.06}} \right)$ 0.64 ± 0.02 0.90 ± 0.02
BIS+logRHK′${\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M3/2 M1/2 –212.03 (−215.82−3.73+3.17)$\left( { - 215.82_{ - 3.73}^{ + 3.17}} \right)$ 0.65 ± 0.02 0.91 ± 0.02
FWHM + BIS data-driven 1 M1/2 M3/2 –212.09 (−216.87−3.55+3.22)$\left( { - 216.87_{ - 3.55}^{ + 3.22}} \right)$ 0.64 ± 0.03 0.90 ± 0.02
BIS+logRHK′${\rm{BIS}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ latent 2 ESP M1/2 –212.28 (−215.72−2.92+2.77)$\left( { - 215.72_{ - 2.92}^{ + 2.77}} \right)$ 0.65 ± 0.02 0.90 ± 0.02
phot +logRHK′${\rm{phot}} + \log {\rm{R}}_{{\rm{HK}}}^\prime $ data-driven 2 M3/2 M1/2 –212.37 (−216.35−3.44+3.18)$\left( { - 216.35_{ - 3.44}^{ + 3.18}} \right)$ 0.59 ± 0.02 0.97 ± 0.03

Notes. Only the 30 best models in term of cross-validation scores are shown. The full results are provided in Appendix E (see Section 7).

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