RV data of simulated spectral time series modeled with SDO images. The input seed spectra generated from the PHOENIX synthetic spectral library are used as the inputs of SOAP-GPU (see Sect. 2.2). Top: RV comparison between the SOAP-GPU simulated spectra and HARPS-N solar spectra. The RVs derived from the simulated spectra are highlighted in green while the RVs derived from HARPS-N solar spectra are shown in black. We interpolated the simulated RV time series (in red) to match the HARPS-N solar observation. The blue dashed vertical lines indicate the times of the CCD warm-ups. Bottom: residuals after subtracting simulated RVs from the HARPS-N solar RVs. The RV residuals are divided into three phases: the decreasing cycle 24 activity phase (black), the quiet phase (red), and the new increasing activity phase of cycle 25 (green). The corresponding rms are 0.891 m/s, 0.905 m/s, and 0.775 m/s, respectively. The rms of HARPS-N solar spectra for these three phases are 1.273 m/s, 1.090 m/s, and 1.990 m/s, and are shown here for comparison.