mlsanityData to 13 Oct 2026

Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids

arXiv 2402.08187 ↗First posted 13 Feb 2024cs.LG cs.NA math.NAcited by 7

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Abstract (arXiv)

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding solutions. Deep Operator Network (DeepONet) and Fourier Neural operator, among other models, have been designed with structures suitable for handling functions as inputs and outputs, enabling real-time predictions as surrogate models for solution operators. There has also been significant progress in the research on surrogate models based on graph neural networks (GNNs), specifically targeting the dynamics in time-dependent PDEs. In this paper, we propose GraphDeepONet, an autoregressive model based on GNNs, to effectively adapt DeepONet, which is well-known for successful operator learning. GraphDeepONet exhibits robust accuracy in predicting solutions compared to existing GNN-based PDE solver models. It maintains consistent performance even on irregular grids, leveraging the advantages inherited from DeepONet and enabling predictions on arbitrary grids. Additionally, unlike traditional DeepONet and its variants, GraphDeepONet enables time extrapolation for time-dependent PDE solutions. We also provide theoretical analysis of the universal approximation capability of GraphDeepONet in approximating continuous operators across arbitrary time intervals.

Key facts. Cited by 7 papers in the map (data through 13 Oct 2026). Builds on 34 of its 51 references that are in the map. First posted on arXiv 13 Feb 2024.

Builds on

34 of 51 references.

References · 34

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22 more
  1. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 406
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Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2025: 4; 2026: 3.

7 papers.

  1. 2025FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learningcited by 7
  2. 2025DeepONet Augmented by Randomized Neural Networks for Efficient Operator Learning in PDEscited by 1
  3. 2025ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensorscited by 1
  4. 2025SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Samplingcited by 1
  5. 2026Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domainscited by 0
  6. 2026No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Studycited by 0
  7. 2026Learning PDE Dynamics between Submanifolds Using Green's Observation Operatorscited by 0