  Point sources (PS) are one of the main contaminants to the recovery of the
cosmic microwave background (CMB) signal at small scales, and their detection
is important for the next generation of CMB experiments. We develop a method
(PoSeIDoN) based on fully convolutional networks to detect PS in realistic
simulations, and we compare its performance against one of the most used PS
detection method, the Mexican hat wavelet 2 (MHW2). We produce realistic
simulations of PS taking into account contaminating signals as the CMB, the
cosmic infrared background, the Galactic thermal emission, the thermal
Sunyaev-Zel'dovich effect, and the instrumental and PS shot noises. We first
produce a set of training simulations at 217 GHz to train the network. Then we
apply both PoSeIDoN and the MHW2 to recover the PS in the validating
simulations at all 143, 217, and 353 GHz, comparing the results by estimating
the reliability, completeness, and flux density accuracy and by computing the
receiver operating characteristic curves. In the extra-galactic region with a
30{\deg} galactic cut, the network successfully recovers PS at 90% completeness
corresponding to 253, 126, and 250 mJy for 143, 217, and 353 GHz respectively.
The MHW2 with a 3$\sigma$ flux density detection limit recovers PS up to 181,
102, and 153 mJy at 90% completeness. In all cases PoSeIDoN produces a much
lower number of spurious sources with respect to MHW2. The results on spurious
sources for both techniques worsen when reducing the galactic cut to 10{\deg}.
Our results suggest that using neural networks is a very promising approach for
detecting PS, providing overall better results in dealing with spurious sources
with respect to usual filtering approaches. Moreover, PoSeIDoN gives
competitive results even at nearby frequencies where the network was not
trained.
