Predicting reliable H$_2$ column density maps from molecular line data using machine learning

The total mass estimate of molecular clouds suffers from the uncertainty in the H$_2$-CO conversion factor, the so-called $X_{\rm CO}$ factor, which is used to convert the $^{12}$CO (1--0) integrated intensity to the H$_2$ column density. We demonstrate the machine learning's ability to predict the H$_2$ column density from the $^{12}$CO, $^{13}$CO, and C$^{18}$O (1--0) data set of four star-forming molecular clouds; Orion A, Orion B, Aquila, and M17. When the training is performed on a subset of each cloud, the overall distribution of the predicted column density is consistent with that of the Herschel column density. The total column density predicted and observed is consistent within 10\%, suggesting that the machine learning prediction provides a reasonable total mass estimate of each cloud. However, the distribution of the column density for values $> \sim 2 \times 10^{22}$ cm$^{-2}$, which corresponds to the dense gas, could not be predicted well. This indicates that molecular line observations tracing the dense gas are required for the training. We also found a significant difference between the predicted and observed column density when we created the model after training the data on different clouds. This highlights the presence of different $X_{\rm CO}$ factors between the clouds, and further training in various clouds is required to correct for these variations. We also demonstrated that this method could predict the column density toward the area not observed by Herschel if the molecular line and column density maps are available for the small portion, and the molecular line data are available for the larger areas.