  The circum-galactic medium (CGM) can feasibly be mapped by multiwavelength
surveys covering broad swaths of the sky. With multiple large datasets becoming
available in the near future, we develop a likelihood-free Deep Learning
technique using convolutional neural networks (CNNs) to infer broad-scale
physical properties of a galaxy's CGM and its halo mass for the first time.
Using CAMELS (Cosmology and Astrophysics with MachinE Learning Simulations)
data, including IllustrisTNG, SIMBA, and Astrid models, we train CNNs on Soft
X-ray and 21-cm (HI) radio 2D maps to trace hot and cool gas, respectively,
around galaxies, groups, and clusters. Our CNNs offer the unique ability to
train and test on ''multifield'' datasets comprised of both HI and X-ray maps,
providing complementary information about physical CGM properties and improved
inferences. Applying eRASS:4 survey limits shows that X-ray is not powerful
enough to infer individual halos with masses $\log(M_{\rm{halo}}/M_{\odot}) <
12.5$. The multifield improves the inference for all halo masses. Generally,
the CNN trained and tested on Astrid (SIMBA) can most (least) accurately infer
CGM properties. Cross-simulation analysis -- training on one galaxy formation
model and testing on another -- highlights the challenges of developing CNNs
trained on a single model to marginalize over astrophysical uncertainties and
perform robust inferences on real data. The next crucial step in improving the
resulting inferences on physical CGM properties hinges on our ability to
interpret these deep-learning models.
