# Conservative Hybrid Graph Networks for Process Systems with Learned Routing

arXiv: https://arxiv.org/abs/2608.28896 · HTML: https://mlsanity.com/paper/2608.28896/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [The why, how, and when of representations for complex systems](https://mlsanity.com/paper/2006.02870/) (2020)
- [Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems](https://mlsanity.com/paper/2211.05520/) (2022)
- [X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulation](https://mlsanity.com/paper/2411.17164/) (2024)
- [Modeling Dynamic Environments with Scene Graph Memory](https://mlsanity.com/paper/2305.17537/) (2023)
- [Graph Neural PDE Solvers with Conservation and Similarity-Equivariance](https://mlsanity.com/paper/2405.16183/) (2024)
- [Neural Hybrid Automata: Learning Dynamics with Multiple Modes and Stochastic Transitions](https://mlsanity.com/paper/2106.04165/) (2021)
- [Graph Neural Network Based Surrogate Model of Physics Simulations for Geometry Design](https://mlsanity.com/paper/2302.00557/) (2023)
- [An Operator-Consistent Graph Neural Network for Learning Diffusion Dynamics on Irregular Meshes](https://mlsanity.com/paper/2512.11860/) (2025)

## Abstract (arXiv)

Industrial process networks do not maintain a single effective topology while operating: streams are throttled or bypassed, and units move between idle, transition, and active regimes. Models of such systems are typically trained on measured state trajectories while the operating mechanisms that generated them remain latent, and an unconstrained graph network can fit such a trajectory without assigning stable physical meaning to the recovered routing. We address both problems with the Conservative Hybrid Graph Network (CHGN), which learns routing, regime assignment, and removal rates as data-driven surrogates and inserts them into a fixed transport equation, so that the mass balance holds by construction for any predicted routing. CHGN trained on networks of 10-20 nodes transfers zero-shot to unseen graphs of 25-40 nodes without retraining, reaching an RMSE of 2.1e-3 against 6e-2 to 9e-2 for GNN baselines under the same protocol, with a gate MAE of 7.9e-3 and regime accuracy of 94.3% (1.2e-2 and 96.4% respectively on the fixed training topology). On a fluid-mixing pilot plant, CHGN improves on a persistence baseline for held-out physical faults but does not predict manual interventions, for which the governing valve actions are unobserved. The model therefore transfers across process topologies without retraining and exposes the latent mechanisms governing plant behaviour to inspection.