We describe the development of machine-learned potentials of atmospheric gases with flexible monomers for molecular simulations. A recently suggested permutationally invariant polynomial neural network (PIP-NN) approach is utilized to represent the full-dimensional two-body component of the dimer energy. To ensure the asymptotic zero-interaction limit, a tailored subset of the full invariant polynomial basis set is utilized and their variables are modified to achieve a better fit of the correct asymptotic behavior at a long range. The new technique is used to build full-dimensional potentials for the two-body N2−Ar and N2−CH4 interactions by fitting databases of ab initio energies calculated at the coupled-cluster level of theory. The second virial coefficients with full account of molecular flexibility effects are then calculated within the classical framework using the PIP-NN potential surfaces. To showcase the advantages of the PIP-NN method, we compare its accuracy and computational efficiency to several kernel-based and neural-network-based approaches using the MD17 database of energies and forces for ethanol. For large training set sizes, the PIP-NN models attain the best accuracy among examined models, and the computation time is shown to be comparable to that of the PIP regression model and several orders of magnitude faster than the quickest alternatives.