Optical Cross-Match of SRG/eROSITA X-ray Sources Using the Deep Lockman Hole Survey as an Example

We present a method for the optical identification of sources detected in wide-field X-ray sky surveys. We have constructed and trained a neural network model to characterise the photometric attributes of the populations of optical counterparts of X-ray sources and optical field objects. The photometric information processing result is used for the probabilistic cross-match of X-ray sources with optical DESI Legacy Imaging Surveys sources. The efficiency of the method is illustrated using the SRG/eROSITA Survey of Lockman Hole. To estimate the accuracy of the method, we have produced a validation sample based on the Chandra and XMM-Newton catalogues of X-ray sources. The cross-match precision in our method reaches 94% for the entire X-ray catalogue and 97% for sources with a flux $F_{\rm x, 0.5-2}>10^{-14}$ erg/s/cm$^2$. We discuss the further development of the optical identification model and the steps needed for its application to the SRG/eROSITA all-sky survey data.