# DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systems

arXiv: https://arxiv.org/abs/2209.10622 · HTML: https://mlsanity.com/paper/2209.10622/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [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)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectories](https://mlsanity.com/paper/2202.07176/) (2022)
- [AST-GCN: Attribute-Augmented Spatiotemporal Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/2011.11004/) (2020)
- [A data-centric weak supervised learning for highway traffic incident detection](https://mlsanity.com/paper/2112.09792/) (2021)

## Built on by (most cited first, 14 of 14)

- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks](https://mlsanity.com/paper/2402.15406/) (2024)
- [D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators](https://mlsanity.com/paper/2310.18888/) (2023)
- [Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profiles](https://mlsanity.com/paper/2306.00810/) (2023)
- [GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications](https://mlsanity.com/paper/2406.03569/) (2024)
- [Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids](https://mlsanity.com/paper/2402.08187/) (2024)
- [Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operators](https://mlsanity.com/paper/2410.24162/) (2024)
- [A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients](https://mlsanity.com/paper/2311.03639/) (2023)
- [Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decomposition](https://mlsanity.com/paper/2511.23037/) (2025)
- [Deep operator network models for predicting post-burn contraction](https://mlsanity.com/paper/2411.14555/) (2024)
- [Discretization-independent operator learning for partial differential equations](https://mlsanity.com/paper/2507.07292/) (2025)
- [Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory](https://mlsanity.com/paper/2509.10378/) (2025)
- [DeepEOSNet: Capturing the dependency on thermodynamic state in property prediction tasks](https://mlsanity.com/paper/2509.17018/) (2025)
- [A Unified Mamba--MoE Surrogate for Closed-Loop Simulation and Measurement-Window Forecasting of Inverter Transients](https://mlsanity.com/paper/2608.15051/) (2026)

## Abstract (arXiv)

This paper develops a Deep Graph Operator Network (DeepGraphONet) framework that learns to approximate the dynamics of a complex system (e.g. the power grid or traffic) with an underlying sub-graph structure. We build our DeepGraphONet by fusing the ability of (i) Graph Neural Networks (GNN) to exploit spatially correlated graph information and (ii) Deep Operator Networks~(DeepONet) to approximate the solution operator of dynamical systems. The resulting DeepGraphONet can then predict the dynamics within a given short/medium-term time horizon by observing a finite history of the graph state information. Furthermore, we design our DeepGraphONet to be resolution-independent. That is, we do not require the finite history to be collected at the exact/same resolution. In addition, to disseminate the results from a trained DeepGraphONet, we design a zero-shot learning strategy that enables using it on a different sub-graph. Finally, empirical results on the (i) transient stability prediction problem of power grids and (ii) traffic flow forecasting problem of a vehicular system illustrate the effectiveness of the proposed DeepGraphONet.