  Gas network planning optimization under emission constraints prioritizes gas
supply with the least CO$_2$ intensity. As this problem includes complex
physical laws of gas flow, standard optimization solvers cannot guarantee
convergence to a feasible solution. To address this issue, we develop an
input-convex neural network (ICNN) aided optimization routine which
incorporates a set of trained ICNNs approximating the gas flow equations with
high precision. Numerical tests on the Belgium gas network demonstrate that the
ICNN-aided optimization dominates non-convex and relaxation-based solvers, with
larger optimality gains pertaining to stricter emission targets. Moreover,
whenever the non-convex solver fails, the ICNN-aided optimization provides a
feasible solution to network planning.
