Paper Citation Record · LEDGER

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling

As of 13 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 1 inbound Pith citation observation for arXiv:2506.12790.

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

pith.paper-citation-record.v1
2506.12790 v1

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T00:48:17.483947Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:58:28.189385Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T17:58:28.548968Z

Reference resolution

44 of 44 outbound references displayed

verified exact0
verified fuzzy11
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation defa42e7-89e4-4729-ba77-7d7200d56a27 · outbound

This paper cites SIAM, 2007.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling SIAM, 2007

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:13.857285Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51b3d690-9c70-4712-8c91-6f4f77ba635e · outbound

This paper cites Cambridge university press, 2002.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Cambridge university press, 2002

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:19.278382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 36f38325-6939-42dc-84eb-af245b1661e1 · outbound

This paper cites An introduction to the finite element method.New York, 27(14), 1993.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling An introduction to the finite element method.New York, 27(14), 1993

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:19.184131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 91c5c4fa-a777-4028-9136-2062a6e40f65 · outbound

This paper cites Workshop report on basic research needs for scientific machine learning: Core technologies for artificial intelligence.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Workshop report on basic research needs for scientific machine learning: Core technologies for artificial intelligence

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.048910Z

Source-reported events for the cited work

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Observation 49729e9a-412f-41c7-afd6-ae8fe078c3c9 · outbound

This paper cites Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.109645Z

Source-reported events for the cited work

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Observation 88f16009-c61b-44a1-bab5-9e29e4dd91c4 · outbound

This paper cites Neural operators for accelerating scientific simulations and design.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Neural operators for accelerating scientific simulations and design

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.221439Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8a607cf-d39a-4885-ad59-c5b848e2baed · outbound

This paper cites Scientific machine learning through physics–informed neural networks: Where we are and what’s next.Journal of Scientific Computing, 92(3):88, 2022.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Scientific machine learning through physics–informed neural networks: Where we are and what’s next.Journal of Scientific Computing, 92(3):88, 2022

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.284421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f592109-21ac-4e95-8710-0e4fc4e310dc · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.355040Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b60c940-eb25-40ce-a99d-c6fbdb698534 · outbound

This paper cites Pdebench: An extensive benchmark for scientific machine learning.Advances in Neural Information Processing Systems, 35:1596–1611, 2022.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Pdebench: An extensive benchmark for scientific machine learning.Advances in Neural Information Processing Systems, 35:1596–1611, 2022

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.408147Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11306b44-f2ff-4f77-bfeb-b8cc2c00ce86 · outbound

This paper cites Openfwi: Large-scale multi-structural benchmark datasets for full waveform inversion.Advances in Neural Information Processing Systems, 35:6007–6020, 2022.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Openfwi: Large-scale multi-structural benchmark datasets for full waveform inversion.Advances in Neural Information Processing Systems, 35:6007–6020, 2022

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:19.061099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 14fd13ea-cf68-4fa9-88a4-2fb74f422b1e · outbound

This paper cites Understanding training and generalization in deep learning by Fourier analysis.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Understanding training and generalization in deep learning by Fourier analysis

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.598284Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80da34ac-7f48-4490-af01-ff34c7908272 · outbound

This paper cites On the spectral bias of neural networks.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling On the spectral bias of neural networks

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.696067Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4eda75dd-581f-4ecd-82fa-c729426d821f · outbound

This paper cites Overview frequency principle/spectral bias in deep learning.Communications on Applied Mathematics and Computation, pages 1–38, 2024.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Overview frequency principle/spectral bias in deep learning.Communications on Applied Mathematics and Computation, pages 1–38, 2024

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.807559Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db9c57fa-a9db-438f-baf2-cdb4a29e68bb · outbound

This paper cites Im- plicit neural representations with periodic activation functions.Advances in neural information processing systems, 33:7462–7473, 2020.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Im- plicit neural representations with periodic activation functions.Advances in neural information processing systems, 33:7462–7473, 2020

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:14.946122Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 794d2221-a7b6-4e45-8883-744e401062a9 · outbound

This paper cites Fourier features let networks learn high frequency functions in low dimensional domains.Advances in neural information processing systems, 33:7537–7547, 2020.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Fourier features let networks learn high frequency functions in low dimensional domains.Advances in neural information processing systems, 33:7537–7547, 2020

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.028091Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce2898e3-81af-4ba2-872b-5d299edc762d · outbound

This paper cites Wire: Wavelet implicit neural representations.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Wire: Wavelet implicit neural representations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:18.944448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f8f58e4c-bd67-4153-8ed9-0b1160ebcb3e · outbound

This paper cites From data to functa: Your data point is a function and you can treat it like one.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling From data to functa: Your data point is a function and you can treat it like one

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.227776Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70a320f3-5ee7-4ddd-a41a-18d1cd92cfa9 · outbound

This paper cites Film: Visual reasoning with a general conditioning layer.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Film: Visual reasoning with a general conditioning layer

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.285570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30ec4a7c-017d-4326-9dbc-6a354ee889bc · outbound

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

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.335878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4edf7273-81a1-49e4-90c5-2b381c740c7e · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Fourier Neural Operator for Parametric Partial Differential Equations

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.360376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a50e2e98-ca95-4671-b16e-95d8b070e16f · outbound

This paper cites Factorized fourier neural operators.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Factorized fourier neural operators

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:18.834435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f092d03f-ff75-4a9f-99f9-6fe3a56ecef7 · outbound

This paper cites Continuous PDE Dynamics Forecasting with Implicit Neural Representations.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Continuous PDE Dynamics Forecasting with Implicit Neural Representations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.595813Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e655f8d2-b016-4e24-b236-c47af19eec99 · outbound

This paper cites Gridmix: Exploring spatial modulation for neural fields in pde modeling.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Gridmix: Exploring spatial modulation for neural fields in pde modeling

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:18.749761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7ec06db6-344d-4da0-8e34-bc21fd2c3004 · outbound

This paper cites an unresolved cited work.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.789974Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41b4584c-3155-4131-8085-91420745e389 · outbound

This paper cites Nerf: Representing scenes as neural radiance fields for view synthesis.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Nerf: Representing scenes as neural radiance fields for view synthesis

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.895354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17bfcfb5-49b7-4b85-9b5c-83c402c94c94 · outbound

This paper cites Neural tangent kernel: Convergence and generalization in neural networks.Advances in neural information processing systems, 31, 2018.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Neural tangent kernel: Convergence and generalization in neural networks.Advances in neural information processing systems, 31, 2018

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:15.974092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e2663ad-e6d0-49a4-9f3e-b314ab6e9913 · outbound

This paper cites Neural networks fail to learn periodic functions and how to fix it.Advances in Neural Information Processing Systems, 33:1583–1594, 2020.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Neural networks fail to learn periodic functions and how to fix it.Advances in Neural Information Processing Systems, 33:1583–1594, 2020

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:18.643818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 375daffb-adc2-4699-9eed-661ad4a37b0e · outbound

This paper cites Deepsdf: Learning continuous signed distance functions for shape representation.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Deepsdf: Learning continuous signed distance functions for shape representation

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.190039Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2efd7850-face-4e24-bba5-13b3d2eaed65 · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.288042Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bba8b79d-9263-4406-a51a-0a200a827f28 · outbound

This paper cites Multiwavelet-based operator learning for differential equations.Advances in neural information processing systems, 34:24048–24062, 2021.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Multiwavelet-based operator learning for differential equations.Advances in neural information processing systems, 34:24048–24062, 2021

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.375156Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a522997d-6762-4c4b-828d-3c9493889fd5 · outbound

This paper cites Wavelet neural operator: a neural operator for parametric partial differential equations.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Wavelet neural operator: a neural operator for parametric partial differential equations

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.384195Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a224aad-301d-4364-85d4-ec835e3f44ee · outbound

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

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.457876Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fe2b8c1-321a-4239-8306-cb707fe7a4c3 · outbound

This paper cites Learning Mesh-Based Simulation with Graph Networks.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Learning Mesh-Based Simulation with Graph Networks

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.563337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee22ee36-0156-4d34-8788-45744ae6c18c · outbound

This paper cites Fourier neural operator with learned deformations for pdes on general geometries.Journal of Machine Learning Research, 24(388):1–26, 2023.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Fourier neural operator with learned deformations for pdes on general geometries.Journal of Machine Learning Research, 24(388):1–26, 2023

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.612312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 668e4951-e29f-4e07-89ee-914f7d57e9ba · outbound

This paper cites Geometry-informed neural operator for large-scale 3d pdes.Advances in Neural Information Processing Systems, 36, 2024.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Geometry-informed neural operator for large-scale 3d pdes.Advances in Neural Information Processing Systems, 36, 2024

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:18.509125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 82e2fd77-7fb1-493b-8d0e-36a419078937 · outbound

This paper cites Operator learning with neural fields: Tackling pdes on general geometries.Advances in Neural Information Processing Systems, 36:70581–70611, 2023.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Operator learning with neural fields: Tackling pdes on general geometries.Advances in Neural Information Processing Systems, 36:70581–70611, 2023

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:18.368711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 09321d87-a509-45f2-8af4-f788d8345b40 · outbound

This paper cites Spatial Functa: Scaling Functa to ImageNet Classification and Generation.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Spatial Functa: Scaling Functa to ImageNet Classification and Generation

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.874471Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 97eda095-2d8f-4c17-a1e1-b428dd83eb73 · outbound

This paper cites Improved implicit neural representation with fourier reparameterized training.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Improved implicit neural representation with fourier reparameterized training

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:16.990853Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5618ee78-4edb-464b-9ffe-fca0c2455055 · outbound

This paper cites An overview of full-waveform inversion in exploration geophysics.Geophysics, 74(6):WCC1–WCC26, 2009.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling An overview of full-waveform inversion in exploration geophysics.Geophysics, 74(6):WCC1–WCC26, 2009

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:17.052964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84d0522c-2b89-48fa-b0f9-c78e671caa07 · outbound

This paper cites Model-agnostic meta-learning for fast adap- tation of deep networks.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Model-agnostic meta-learning for fast adap- tation of deep networks

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:17.118245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2fbf9093-88b6-4659-8e2b-cff26a87a348 · outbound

This paper cites Fast context adaptation via meta-learning.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Fast context adaptation via meta-learning

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:18.180741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e5de6b93-45de-4f7b-bb03-aa231ab1f458 · outbound

This paper cites U-net: Convolutional networks for biomedical image segmentation.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling U-net: Convolutional networks for biomedical image segmentation

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-07T00:48:17.283684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 309430c6-04b5-4e37-9565-08f466d988ca · outbound

This paper cites On the benefits of memory for modeling time-dependent PDEs.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling On the benefits of memory for modeling time-dependent PDEs

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:48:17.950337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1dadd2e1-9250-4fa5-81a2-f29db190184b · outbound

This paper cites Inducing point operator transformer: A flexible and scalable architecture for solving pdes.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling Inducing point operator transformer: A flexible and scalable architecture for solving pdes

Reference 44

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T00:48:17.797262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 578126b3-efe0-42e6-a9c3-846c17fe9d2c · inbound

ELMZip: Onboard Satellite Image Compression via Extreme Learning Machines for Efficient Downlink cites this paper.

ELMZip: Onboard Satellite Image Compression via Extreme Learning Machines for Efficient Downlink PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-10T17:58:28.609500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.