  The dynamics in the photosphere is governed by the multi-scale turbulent
convection termed as granulation and supergranulation. It is important to
derive 3-dimensional velocity vectors to understand the nature of the turbulent
convection. However, it is difficult to obtain the velocity component
perpendicular to the line-of-sight, which corresponds to the horizontal
velocity in disk center observations. We developed a convolutional neural
network model with a multi-scale deep learning architecture. The method
consists of multiple convolutional kernels with various sizes of the receptive
fields, and it performs convolution for spatial and temporal axes. The network
is trained with data from three different numerical simulations of turbulent
convection, and we introduced a coherence spectrum to assess the horizontal
velocity fields that were derived at each spatial scale. The multi-scale deep
learning method successfully predicts the horizontal velocities for each
convection simulation in terms of the global-correlation-coefficient, which is
often used for evaluating the prediction accuracy of the methods. The coherence
spectrum reveals the strong dependence of the correlation coefficients on the
spatial scales. Although coherence spectra are higher than 0.9 for large-scale
structures, they drastically decrease to less than 0.3 for small-scale
structures wherein the global-correlation-coefficient indicates a high value of
approximately 0.95. We determined that this decrease in the coherence spectrum
occurs around the energy injection scales. The accuracy for the small-scale
structures is not guaranteed solely by the global-correlation-coefficient. To
improve the accuracy in small-scales, it is important to improve the loss
function for enhancing the small-scale structures and to utilize other physical
quantities related to the non-linear cascade of convective eddies as input
data.
