mlsanityData to 14 Oct 2026

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

arXiv 2209.10622 ↗First posted 21 Sep 2022cs.LGcited by 14

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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.

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

24 of 49 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Graph Attention Networkscited by 8,923
  4. 2017Inductive Representation Learning on Large Graphscited by 6,320
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  8. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
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12 more
  1. 2020Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networkscited by 566
  2. 2018T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Predictioncited by 401
  3. 2016Learning Convolutional Neural Networks for Graphscited by 314
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  6. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 140
  7. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  8. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 96
  9. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 89
  10. 2022DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectoriescited by 30
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  12. 2021A data-centric weak supervised learning for highway traffic incident detectioncited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 5; 2025: 4; 2026: 1.

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  1. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  2. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  3. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  4. 2023Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profilescited by 10
  5. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
  6. 2024Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular gridscited by 7
  7. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  8. 2023A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficientscited by 4
  9. 2025Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decompositioncited by 2
  10. 2024Deep operator network models for predicting post-burn contractioncited by 1
  11. 2025Discretization-independent operator learning for partial differential equationscited by 0
  12. 2025Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theorycited by 0
2 more
  1. 2025DeepEOSNet: Capturing the dependency on thermodynamic state in property prediction taskscited by 0
  2. 2026A Unified Mamba--MoE Surrogate for Closed-Loop Simulation and Measurement-Window Forecasting of Inverter Transientscited by 0