mlsanityData to 7 Oct 2026

HAMLET: Graph Transformer Neural Operator for Partial Differential Equations

arXiv 2402.03541 ↗First posted 5 Feb 2024cs.LG cs.NA math.NAcited by 24

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Abstract (arXiv)

We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly incorporate differential equation information into the solution process. This modularity enhances parameter correspondence control, making HAMLET adaptable to PDEs of arbitrary geometries and varied input formats. Notably, HAMLET scales effectively with increasing data complexity and noise, showcasing its robustness. HAMLET is not just tailored to a single type of physical simulation, but can be applied across various domains. Moreover, it boosts model resilience and performance, especially in scenarios with limited data. We demonstrate, through extensive experiments, that our framework is capable of outperforming current techniques for PDEs.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 54 of its 68 references that are in the map. First posted on arXiv 5 Feb 2024.

Builds on

54 of 68 references.

References · 54

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Citing papers per year: 2024: 4; 2025: 11; 2026: 9.

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  1. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  2. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  3. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 20
  4. 2024Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEscited by 16
  5. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  6. 2025FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learningcited by 7
  7. 2025Accurate and scalable deep Maxwell solvers using multilevel iterative methodscited by 5
  8. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  9. 2025Method of Manufactured Learning for Solver-free Training of Neural Operatorscited by 3
  10. 2025GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equationscited by 2
  11. 2025PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencilscited by 2
  12. 2025A Mathematical Explanation of Transformerscited by 2
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  4. 2026Benchmarking Long Roll-outs of Auto-regressive Neural Operators for the Compressible Navier-Stokes Equations with Conserved Quantity Correctioncited by 1
  5. 2026Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEscited by 1
  6. 2024ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equationscited by 0
  7. 2025Connecting the geometry and dynamics of many-body complex systems with message passing neural operatorscited by 0
  8. 2026SpectraKAN: Conditioning Spectral Operatorscited by 0
  9. 2026FlowForge: A Staged Local Rollout Engine for Flow-Field Predictioncited by 0
  10. 2026CATO: Charted Attention for Neural PDE Operatorscited by 0
  11. 2026Neural Scaling Laws of Transformer Operator Networkcited by 0
  12. 2026RINS: Residual-Image Neural Subspace Solvers for Large Sparse Linear Systemscited by 0