Emission-Constrained Optimization of Gas Systems with Input-Convex Neural Networks

Planning optimization of gas networks under emission constraints prioritizes gas supply with the smallest emission footprint. As this problem includes complex gas flow physical laws, standard optimization solvers cannot guarantee convergence to a feasible solution, especially under strict emission constraints. 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.