# A Graph-Enhanced DeepONet Approach for Real-Time Estimating Hydrogen-Enriched Natural Gas Flow under Variable Operations

arXiv: https://arxiv.org/abs/2504.08816 · HTML: https://mlsanity.com/paper/2504.08816/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 9 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 1 of 1)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)

## Abstract (arXiv)

Blending green hydrogen into natural gas presents a promising approach for renewable energy integration and fuel decarbonization. Accurate estimation of hydrogen fraction in hydrogen-enriched natural gas (HENG) pipeline networks is crucial for operational safety and efficiency, yet it remains challenging due to complex dynamics. While existing data-driven approaches adopt end-to-end architectures for HENG flow state estimation, their limited adaptability to varying operational conditions hinders practical applications. To this end, this study proposes a graph-enhanced DeepONet framework for the real-time estimation of HENG flow, especially hydrogen fractions. First, a dual-network architecture, called branch network and trunk network, is employed to characterize operational conditions and sparse sensor measurements to estimate the HENG state at targeted locations and time points. Second, a graph-enhance branch network is proposed to incorporate pipeline topology, improving the estimation accuracy in large-scale pipeline networks. Experimental results demonstrate that the proposed method achieves superior estimation accuracy for HCNG flow under varying operational conditions compared to conventional approaches.