Paper Citation Record · LEDGER

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery

As of 21 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 2 inbound Pith citation observations for arXiv:2505.23106.

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

pith.paper-citation-record.v1
2505.23106 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:02:04.167969Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:00:10.883289Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T14:57:35.216417Z

Reference resolution

29 of 29 outbound references displayed

verified exact6
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b809371e-b125-4fb1-90c3-e2cbb1a98329 · outbound

This paper cites (b): displacement fields (second row) ux corresponding to the same loading field (first row) fx.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery (b): displacement fields (second row) ux corresponding to the same loading field (first row) fx

Reference 2

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Observation 30c6c1d4-cac4-4619-85f3-e543cd232ed8 · outbound

This paper cites Note that NIPS is conceptually related to the Performer (Choromanski et al., 2020), which introduces kernel-based approx- imations for efficient self-attention.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Note that NIPS is conceptually related to the Performer (Choromanski et al., 2020), which introduces kernel-based approx- imations for efficient self-attention

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:02:06.385967Z

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Observation 63837ff7-c5ae-48cc-88e6-a578519279fe · outbound

This paper cites Coupling deep learning with full waveform inversion.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Coupling deep learning with full waveform inversion

Reference 5

Resolution: verified exact; raw_fallback, observed 2026-08-07T13:02:05.818616Z

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Observation 2727b81d-255f-46cf-8366-60e05368666b · outbound

This paper cites Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

Reference 7

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Observation 025f15b7-86e3-472f-be24-ea7a452c2a37 · outbound

This paper cites Reinforced inverse scat- tering.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Reinforced inverse scat- tering

Reference 8

Resolution: verified exact; raw_fallback, observed 2026-08-07T13:02:05.501485Z

Source-reported events for the cited work

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Observation 5e8e36de-c3d3-4011-9c13-6a63610e7be9 · outbound

This paper cites PolySketchFormer: Fast Transformers via Sketching Polynomial Kernels.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery PolySketchFormer: Fast Transformers via Sketching Polynomial Kernels

Reference 9

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Observation 9bb18386-41a2-4832-872b-5fd7f6843dc3 · outbound

This paper cites Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing

Reference 12

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Observation caa14c7f-ac78-4130-ad7a-729c87e48da2 · outbound

This paper cites Transformer learns the cross-task prior and regularization for in-context learning.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Transformer learns the cross-task prior and regularization for in-context learning

Reference 13

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Source-reported events for the cited work

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Observation f93530ee-be33-4059-b338-becc165e0781 · outbound

This paper cites M., Letey, M.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery M., Letey, M

Reference 15

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Observation cf77c6d6-49a0-48af-a34f-01db6000c54b · outbound

This paper cites Neural Inverse Operators for Solving PDE Inverse Problems.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Neural Inverse Operators for Solving PDE Inverse Problems

Reference 16

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Observation d9e3dfaa-819f-4808-9c09-98a1e00fba48 · outbound

This paper cites Deep synthesis regularization of inverse problems.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Deep synthesis regularization of inverse problems

Reference 17

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Observation c20e4211-9c9c-492b-8768-ce13a917b166 · outbound

This paper cites IAE-Net: Integral Autoencoders for Discretization-Invariant Learning.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery IAE-Net: Integral Autoencoders for Discretization-Invariant Learning

Reference 18

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This paper cites Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation

Reference 19

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Observation e11dc1a2-2d37-47b9-a01a-9e1d9f46eef8 · outbound

This paper cites Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:02:04.636625Z

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Observation ec6231d9-dc94-4ad3-8b1e-c298660bfcc9 · outbound

This paper cites Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T13:02:03.735194Z

Source-reported events for the cited work

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Observation 55d31764-e49a-4362-acef-962ca6a5b5d6 · outbound

This paper cites PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T13:02:03.788505Z

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Observation caf6274c-8782-4a10-8b50-656c0d9b9a6a · outbound

This paper cites PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T13:02:03.841967Z

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Observation 3896e4e5-1105-4c7d-8353-e5b2a5cd056f · outbound

This paper cites Bold numbers highlight the best method.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Bold numbers highlight the best method

Reference 26

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Observation 314494a5-c105-4328-98ed-c905028cc4c2 · outbound

This paper cites • NAO-f: The NAO-f model follows the same configuration as NAO, except that LayerNorm is applied across both the token and projection dimensions in all layers.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery • NAO-f: The NAO-f model follows the same configuration as NAO, except that LayerNorm is applied across both the token and projection dimensions in all layers

Reference 64

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Observation df3dff21-0546-4646-9389-63d9bdf71802 · outbound

This paper cites Physics-Informed Deep Neural Operator Networks.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Physics-Informed Deep Neural Operator Networks

Reference 1991

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Observation 62b427dc-974e-41a8-bf55-a475aceb9651 · outbound

This paper cites Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network

Reference 2001

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Observation 165ac867-6ee6-4e41-8cd4-abdd43d19958 · outbound

This paper cites MODNO: Multi Operator Learning With Distributed Neural Operators.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery MODNO: Multi Operator Learning With Distributed Neural Operators

Reference 2018

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Observation 18f75e66-21f7-421e-ac63-ab3366e065ad · outbound

This paper cites Let data talk: data-regularized operator learning theory for inverse problems.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Let data talk: data-regularized operator learning theory for inverse problems

Reference 2019

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:02:06.089109Z

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Observation b8e427cd-fd3b-44c3-9330-96dc113afd7a · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 2020

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Observation 3d506c59-4171-472d-b4ca-3eab4c5bb3a6 · outbound

This paper cites Transformer for Partial Differential Equations' Operator Learning.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Transformer for Partial Differential Equations' Operator Learning

Reference 2021

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Observation a51de2d4-652e-4d22-9643-1a22bc6714d5 · outbound

This paper cites Polynormer: Polynomial-Expressive Graph Transformer in Linear Time.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Polynormer: Polynomial-Expressive Graph Transformer in Linear Time

Reference 2022

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Observation 9697a177-ab4b-40e9-b150-349e0ea450c4 · outbound

This paper cites Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

Reference 2023

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Observation 18e3772b-d5b4-4f77-96d6-4d2421f587b2 · outbound

This paper cites Rethinking Attention with Performers.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Rethinking Attention with Performers

Reference 2024

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Observation 69097a3e-9633-485f-82ae-6577d1ac9c9d · outbound

This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 2025

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Pith citing papers

Observation 257aae5d-e01a-4878-a326-d403c99f0943 · inbound

Learning Causal Graphs at Scale: A Foundation Model Approach cites this paper.

Learning Causal Graphs at Scale: A Foundation Model Approach Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery

Reference 2020

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Observation 40d8ba9c-1e4e-4acd-8df5-a349761cfa12 · inbound

A Learning-based Domain Decomposition Method cites this paper.

A Learning-based Domain Decomposition Method Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T14:57:35.222445Z

Source-reported events for the cited work

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