Paper Citation Record · LEDGER

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

As of 18 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 7 inbound Pith citation observations for arXiv:2507.15409.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.15409 v2

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:38:33.034749Z

measured 55 of 55 standing notices

One-hop event checks from named stored sources.

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measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:30:46.884864Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-22T07:34:42.670311Z

Reference resolution

48 of 48 outbound references displayed

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External citation measurements

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Outbound references

Observation 847e3e4d-0384-43c4-8ef0-f7a0a7747a69 · outbound

This paper cites an unresolved cited work.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Unresolved cited work

Reference 1

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Unresolved cited work

Reference 2

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Observation 1f64720e-6643-4e6e-a781-63ec7c36ad92 · outbound

This paper cites Nature Machine Intelligence3(3), 218–229 (2021) https://doi.org/10.1038/ s42256-021-00302-5.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Nature Machine Intelligence3(3), 218–229 (2021) https://doi.org/10.1038/ s42256-021-00302-5

Reference 3

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This paper cites an unresolved cited work.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Unresolved cited work

Reference 4

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Unresolved cited work

Reference 5

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Observation 8709ba4d-202b-46b8-a303-e15a5489ea02 · outbound

This paper cites Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers

Reference 6

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Observation f8701d8c-e09b-49e8-821e-07d11db04e85 · outbound

This paper cites Transactions on Machine Learning 26 Research (2024).

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Transactions on Machine Learning 26 Research (2024)

Reference 7

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Observation e33942ed-01d7-43f8-a7e5-afbe7f6e5d3c · outbound

This paper cites A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions

Reference 8

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Observation 9244c1b4-1edb-4530-b1eb-a316dc336c95 · outbound

This paper cites Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text

Reference 9

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Unresolved cited work

Reference 10

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Observation 9a74aff6-5fca-4717-85da-bbb5e7589482 · outbound

This paper cites Physical Review E111(3), 035304 (2025).

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Physical Review E111(3), 035304 (2025)

Reference 11

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This paper cites LeMON: Learning to Learn Multi-Operator Networks.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations LeMON: Learning to Learn Multi-Operator Networks

Reference 12

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This paper cites PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 13

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This paper cites Proceedings of the National Academy of Sciences120(39), 2310142120 (2023).

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Proceedings of the National Academy of Sciences120(39), 2310142120 (2023)

Reference 14

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Observation 5aac4e2e-6468-4120-9e85-bab93b5a5654 · outbound

This paper cites Journal of Computational Physics519, 113379 (2024) https://doi.org/10.1016/j.jcp.2024.113379.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Journal of Computational Physics519, 113379 (2024) https://doi.org/10.1016/j.jcp.2024.113379

Reference 15

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Observation 2df9fac9-57e4-4442-8827-6d24506dd9e8 · outbound

This paper cites https://arxiv.org/abs/2411.16063.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations https://arxiv.org/abs/2411.16063

Reference 16

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Unresolved cited work

Reference 17

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Observation 843566d4-4122-46cb-a941-ffc7a5e93ca8 · outbound

This paper cites In: Salakhutdinov, R., Kolter, Z., Heller, K., Weller, A., Oliver, N., Scarlett, J., Berkenkamp, F.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations In: Salakhutdinov, R., Kolter, Z., Heller, K., Weller, A., Oliver, N., Scarlett, J., Berkenkamp, F

Reference 18

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This paper cites OmniArch: Building Foundation Model For Scientific Computing.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations OmniArch: Building Foundation Model For Scientific Computing

Reference 19

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This paper cites BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics

Reference 20

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Observation 0d7b9860-e248-47ad-b6af-0aec2db49238 · outbound

This paper cites Advances in Neural Information Processing Systems36, 71242–71262 (2023).

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Advances in Neural Information Processing Systems36, 71242–71262 (2023)

Reference 21

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This paper cites Advances in Neural Information Processing Systems37, 104035–104064 (2024).

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Advances in Neural Information Processing Systems37, 104035–104064 (2024)

Reference 22

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations In: Advances in Neural Information Processing Systems, vol

Reference 23

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This paper cites PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations

Reference 24

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This paper cites Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods

Reference 25

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations preprint (2023)

Reference 26

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This paper cites In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, pp.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, pp

Reference 27

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This paper cites Journal of Machine Learning Research24(388), 1–26 (2023).

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Journal of Machine Learning Research24(388), 1–26 (2023)

Reference 28

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This paper cites arXiv preprint arXiv:2501.19205 (2025).

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations arXiv preprint arXiv:2501.19205 (2025)

Reference 29

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations In: Proceed- ings of ICNN’95 - International Conference on Neural Networks, vol

Reference 30

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations Adam: A Method for Stochastic Optimization

Reference 31

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp

Reference 33

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations In: 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations DeepONet (MLP)

Reference 42

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations 39: Visualization of the divergence-constrained DCR equation on a square domain periodic along both axes and initial conditions violating the divergence constraint

Reference 46

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PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations 41: Visualization of the divergence-constrained wave equation on a square domain periodic along both axes and initial conditions satisfying the divergence constraint

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:38:34.810721Z

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Pith citing papers

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Self-supervised neural operator for solving partial differential equations cites this paper.

Self-supervised neural operator for solving partial differential equations PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Reference 22

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Observation aaf1a791-b4b6-48c0-876d-e03b30b2fe60 · inbound

MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data cites this paper.

MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Reference 68

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jNO: A JAX Library for Neural Operator and Foundation Model Training cites this paper.

jNO: A JAX Library for Neural Operator and Foundation Model Training PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Reference 11

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Tadpole: Autoencoders as Foundation Models for 3D PDEs with Online Learning cites this paper.

Tadpole: Autoencoders as Foundation Models for 3D PDEs with Online Learning PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Reference 8

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Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning cites this paper.

Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Reference 50

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs cites this paper.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Reference 58

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Distillation of Foundation Models for Time-dependent PDEs cites this paper.

Distillation of Foundation Models for Time-dependent PDEs PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Reference 13

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