Paper Citation Record · LEDGER

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

As of 11 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2608.06428.

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

pith.paper-citation-record.v1
2608.06428 v1

Coverage vector

measured 35 of 35 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-10T04:33:16.455001Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

35 of 35 outbound references displayed

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External citation measurements

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Outbound references

Observation a196296f-ee94-443c-b058-c2bf28e6ebc5 · outbound

This paper cites Learn- ing nonlinear operators via DeepONet based on the universal approximation theorem of op- erators.Nature Machine Intelligence, 3(3):218–229, 2021.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Learn- ing nonlinear operators via DeepONet based on the universal approximation theorem of op- erators.Nature Machine Intelligence, 3(3):218–229, 2021

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.333973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c26ee12-ce2f-4338-ad0e-b45c91a7e6fe · outbound

This paper cites Topological deeponets and a generalization of the chen-chen operator approximation theorem.arXiv preprint arXiv:2603.11972, 2026.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Topological deeponets and a generalization of the chen-chen operator approximation theorem.arXiv preprint arXiv:2603.11972, 2026

Reference 2

Resolution: verified exact; raw_fallback, observed 2026-08-10T04:33:16.746740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d49fefd1-1ede-4d01-a9e1-45ee1a6eb630 · outbound

This paper cites On the training and generalization of deep operator networks.SIAM Journal on Scientific Computing, 46(4):C273–C296, 2024.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces On the training and generalization of deep operator networks.SIAM Journal on Scientific Computing, 46(4):C273–C296, 2024

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.892660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 89a5c194-68ee-4810-9fa8-5690ca26eeb1 · outbound

This paper cites Fourier neural operator for parametric partial differential equations.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Fourier neural operator for parametric partial differential equations

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.883307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation cdc7272d-37d3-454a-9df5-1f9c7ee132f9 · outbound

This paper cites Deep neural operators as accurate surrogates for shape optimization.Engineering Applications of Artificial Intelligence, 129:107615, 2024.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Deep neural operators as accurate surrogates for shape optimization.Engineering Applications of Artificial Intelligence, 129:107615, 2024

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.348926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a3bb179-0bac-41af-91ff-714d3baea3c7 · outbound

This paper cites Learning two-phase microstructure evolution using neural operators and autoencoder architectures.npj Computational Materials, 8(1):190, 2022.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Learning two-phase microstructure evolution using neural operators and autoencoder architectures.npj Computational Materials, 8(1):190, 2022

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.353020Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb691f03-fa68-47de-b145-22e93cf40250 · outbound

This paper cites Rethinking materials simulations: Blending direct numerical simulations with neural operators.npj Computational Materials, 10(1):145, 2024.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Rethinking materials simulations: Blending direct numerical simulations with neural operators.npj Computational Materials, 10(1):145, 2024

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.862661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4ef026b4-e4da-4013-8504-f5eac189c63a · outbound

This paper cites Deep operator neural network model predictive control.IEEE Open Journal of Control Systems, 2025.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Deep operator neural network model predictive control.IEEE Open Journal of Control Systems, 2025

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.852514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 593decdb-d2a8-4dc8-9e31-066a18c7c0b3 · outbound

This paper cites Neural Operator Modeling of Platelet Geometry and Stress in Shear Flow.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Neural Operator Modeling of Platelet Geometry and Stress in Shear Flow

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.362477Z

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Observation 8189ade0-f32d-4cdd-88bd-c1e23e624926 · outbound

This paper cites Deep operator learning-based surrogate models for aerothermodynamic analysis of AEDC hypersonic waverider.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Deep operator learning-based surrogate models for aerothermodynamic analysis of AEDC hypersonic waverider

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.366020Z

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Observation 4859811b-a1cc-4892-b991-3117d7afa208 · outbound

This paper cites an unresolved cited work.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.369818Z

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Observation b5935393-252e-402e-b6ed-37485380ea33 · outbound

This paper cites Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.377619Z

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Observation feb5c3f7-b675-4922-ab90-ef9810d813d6 · outbound

This paper cites Universal Differential Equations for Scientific Machine Learning.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Universal Differential Equations for Scientific Machine Learning

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.381029Z

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Observation 3c4d4d92-abed-4705-91a4-29e2e8ce9f85 · outbound

This paper cites Scientific machine learning through physics-informed neural 37 networks: Where we are and what’s next.Journal of Scientific Computing, 92(3):88, 2022.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Scientific machine learning through physics-informed neural 37 networks: Where we are and what’s next.Journal of Scientific Computing, 92(3):88, 2022

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.384577Z

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Observation 3a971b99-0f82-49e7-aa56-4c2e89c65eb5 · outbound

This paper cites Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhat- tacharya, Andrew M.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhat- tacharya, Andrew M

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.837331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c4fbd088-4b23-4514-9c32-e030ecaf335e · outbound

This paper cites Multiwavelet-based operator learning for differential equations.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Multiwavelet-based operator learning for differential equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.827557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0ac75c2e-bf98-4095-a399-6587ab99e2fc · outbound

This paper cites GNOT: A general neural operator transformer for operator learning.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces GNOT: A general neural operator transformer for operator learning

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.817665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ffac0d9c-ba41-4de4-98e3-d1dcd6eb9cf1 · outbound

This paper cites Battaglia.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Battaglia

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.808452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bc15d5cc-9087-4dfb-a851-dfee24ac0701 · outbound

This paper cites Wang, Yuan Yin, Jean- No¨ el Vittaut, and Patrick Gallinari.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Wang, Yuan Yin, Jean- No¨ el Vittaut, and Patrick Gallinari

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.799157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 72f17dfa-d614-4fba-a0b4-0bd308154139 · outbound

This paper cites Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.405840Z

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Observation 16b35581-82a7-4162-9cae-0419e904ec3d · outbound

This paper cites Seidman, Georgios Kissas, Paris Perdikaris, and George J.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Seidman, Georgios Kissas, Paris Perdikaris, and George J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.789397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8e1e72bc-6b78-4440-a4d9-e941b584eec8 · outbound

This paper cites Learning the solution operator of para- metric partial differential equations with physics-informed DeepONets.Science Advances, 7 (40):eabi8605, 2021.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Learning the solution operator of para- metric partial differential equations with physics-informed DeepONets.Science Advances, 7 (40):eabi8605, 2021

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.412607Z

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Observation 602eeecd-a3e4-4922-8039-f91bd3d09f38 · outbound

This paper cites Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.415871Z

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Observation d9ce42ea-c52d-447f-8061-17a87cb1f624 · outbound

This paper cites MIONet: Learning multiple-input operators via tensor product.SIAM Journal on Scientific Computing, 44(6):A3490–A3514, 2022.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces MIONet: Learning multiple-input operators via tensor product.SIAM Journal on Scientific Computing, 44(6):A3490–A3514, 2022

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.419346Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c7a2983-7ca7-4b0d-a1f4-594cebbd584e · outbound

This paper cites SVD perspectives for augmenting DeepONet flexibility and interpretability.Computer Methods in Applied Mechanics and Engineering, 403:115718,.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces SVD perspectives for augmenting DeepONet flexibility and interpretability.Computer Methods in Applied Mechanics and Engineering, 403:115718,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.779331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 169666e6-acb6-42d2-a269-9aa6968805a9 · outbound

This paper cites Multiscale DeepONet for nonlinear operators in oscillatory function spaces for building seismic wave responses.Engineering Structures, 276:115221, 2023.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Multiscale DeepONet for nonlinear operators in oscillatory function spaces for building seismic wave responses.Engineering Structures, 276:115221, 2023

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T04:33:16.769128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d6bfb051-28ce-4b57-9225-b2a90db2bbce · outbound

This paper cites Variable-Input Deep Operator Networks.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Variable-Input Deep Operator Networks

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.433756Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36663e0d-465e-4ae0-a3a4-d73117a7daa9 · outbound

This paper cites BelNet: Basis enhanced learning, a mesh-free neural operator.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces BelNet: Basis enhanced learning, a mesh-free neural operator

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-10T04:33:16.513578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f46dd968-4eb5-4295-a6d0-31831d136c76 · outbound

This paper cites A discretization-invariant extension and analysis of some deep operator networks.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces A discretization-invariant extension and analysis of some deep operator networks

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-10T04:33:16.499957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0010e4fa-84f1-4b0b-b455-4f3f53a9757f · outbound

This paper cites Error estimates for DeepOnets: A deep learning framework in infinite dimensions.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Error estimates for DeepOnets: A deep learning framework in infinite dimensions

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.444644Z

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Observation dbf420ee-4485-4667-9c30-6573db8b35e9 · outbound

This paper cites an unresolved cited work.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-10T04:33:16.756345Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0027325c-5bf5-4b3e-986d-d945e5f6d10e · outbound

This paper cites Physics-Informed Neural Operator for Learning Partial Differential Equations.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 32

Resolution: malformed identifier; no resolver link, observed 2026-08-10T04:33:16.455001Z

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Observation a3240b94-304e-4777-b456-2e081e36c4d2 · outbound

This paper cites an unresolved cited work.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Unresolved cited work

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.373966Z

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Unavailable: canonical work link unavailable.

Observation 08e72bfd-100d-4668-9ccc-76464ba044bf · outbound

This paper cites Error estimates for DeepOnets: A deep learning framework in infinite dimensions.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Error estimates for DeepOnets: A deep learning framework in infinite dimensions

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.448299Z

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Unavailable: canonical work link unavailable.

Observation c0723b6d-d0db-425f-8ceb-09dd0bfe9f34 · outbound

This paper cites an unresolved cited work.

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces Unresolved cited work

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-10T04:33:16.426929Z

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