# Emission-Aware Optimization of Gas Networks: Input-Convex Neural Network Approach

arXiv: https://arxiv.org/abs/2209.08645 · HTML: https://mlsanity.com/paper/2209.08645/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 18 Sep 2022.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability](https://mlsanity.com/paper/1809.03008/) (2018)
- [ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs](https://mlsanity.com/paper/1907.03140/) (2019)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2003.07939/) (2020)
- [State and Parameter Estimation for Natural Gas Pipeline Networks using Transient State Data](https://mlsanity.com/paper/1803.07156/) (2018)
- [An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers](https://mlsanity.com/paper/1805.04414/) (2018)
- [Natural Gas Flow Equations: Uniqueness and an MI-SOCP Solver](https://mlsanity.com/paper/1809.09025/) (2018)
- [Natural Gas Flow Solvers using Convex Relaxation](https://mlsanity.com/paper/1906.01711/) (2019)
- [Decreasing market value of variable renewables can be avoided by policy action](https://mlsanity.com/paper/2002.05209/) (2020)
- [An Uncertainty Management Framework for Integrated Gas-Electric Energy Systems](https://mlsanity.com/paper/2006.14561/) (2020)
- [Stochastic Control and Pricing for Natural Gas Networks](https://mlsanity.com/paper/2010.03283/) (2020)
- [Multi-Stage Linear Decision Rules for Stochastic Control of Natural Gas Networks with Linepack](https://mlsanity.com/paper/2110.02824/) (2021)

## Abstract (arXiv)

Gas network planning optimization under emission constraints prioritizes gas supply with the least CO2 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.