Paper Citation Record · LEDGER

Adversarial Autoencoders in Operator Learning

As of 13 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 0 inbound Pith citation observations for arXiv:2412.07811.

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

pith.paper-citation-record.v1
2412.07811 v1

Coverage vector

measured 52 of 52 reference resolution

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One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

52 of 52 outbound references displayed

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External citation measurements

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Outbound references

Observation 3520c8cc-c5a2-4c7d-b795-e23100eb91fa · outbound

This paper cites Operator Learning: Algorithms and Analysis.

Adversarial Autoencoders in Operator Learning Operator Learning: Algorithms and Analysis

Reference 1

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Observation d6495d50-c190-45d3-8b01-b71079a1f703 · outbound

This paper cites A Mathematical Guide to Operator Learning.

Adversarial Autoencoders in Operator Learning A Mathematical Guide to Operator Learning

Reference 2

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Observation a9f5e8c7-d33f-4d29-9e1c-fef343f74350 · outbound

This paper cites NeuralNetworkApproximationstoSolutionOperatorsforPartialDifferential Equations.

Adversarial Autoencoders in Operator Learning NeuralNetworkApproximationstoSolutionOperatorsforPartialDifferential Equations

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.092430Z

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Observation a2567001-7cb5-4912-a165-8a37a7003416 · outbound

This paper cites Reducing the dimensionality of data with neural networks.

Adversarial Autoencoders in Operator Learning Reducing the dimensionality of data with neural networks

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.084463Z

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Observation 0fa52ad2-4b04-49e2-bcb4-088ea17f9134 · outbound

This paper cites “Learning internal representa- tions by error propagation, parallel distributed processing, explorations in the microstructure of cognition, ed.

Adversarial Autoencoders in Operator Learning “Learning internal representa- tions by error propagation, parallel distributed processing, explorations in the microstructure of cognition, ed

Reference 5

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Observation 87404ea4-958d-4367-ad6b-91566e5e9286 · outbound

This paper cites Auto-Encoding Variational Bayes.

Adversarial Autoencoders in Operator Learning Auto-Encoding Variational Bayes

Reference 6

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Source-reported events for the cited work

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Observation 7aa629cf-6731-4a78-b94b-113cda3b06e7 · outbound

This paper cites Adversarial Autoencoders.

Adversarial Autoencoders in Operator Learning Adversarial Autoencoders

Reference 7

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Observation 8017119f-68f2-493e-a0b7-ee60e8540894 · outbound

This paper cites Binary cross entropy with deep learning technique for image classification.

Adversarial Autoencoders in Operator Learning Binary cross entropy with deep learning technique for image classification

Reference 8

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Observation c710fe8c-8677-4817-93c0-3edca4fe5563 · outbound

This paper cites Generative deep learning: teaching machines to paint.

Adversarial Autoencoders in Operator Learning Generative deep learning: teaching machines to paint

Reference 9

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Observation a331c81a-4385-4555-8a53-9107c5fc1f27 · outbound

This paper cites LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators.

Adversarial Autoencoders in Operator Learning LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators

Reference 10

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Observation e8d85829-23d8-48a9-bb84-4a987d39e781 · outbound

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

Adversarial Autoencoders in Operator Learning Error estimates for deep- onets: A deep learning framework in infinite dimensions

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.051430Z

Source-reported events for the cited work

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Observation 7c747eee-129d-4a34-8c32-74d70878c9fd · outbound

This paper cites A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials.

Adversarial Autoencoders in Operator Learning A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.042899Z

Source-reported events for the cited work

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Observation 341db8d3-c6ed-47a1-8ec9-1f50ba8e1e64 · outbound

This paper cites Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads.

Adversarial Autoencoders in Operator Learning Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.034567Z

Source-reported events for the cited work

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Observation a6b4b50d-3016-4ac3-80f7-cfbc316f40f0 · outbound

This paper cites Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids.

Adversarial Autoencoders in Operator Learning Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids

Reference 14

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Observation 67c09cdc-59d1-43e5-b035-a788f3f42749 · outbound

This paper cites A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data.

Adversarial Autoencoders in Operator Learning A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.026039Z

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Observation 22776016-cf89-494b-a635-b0d026e98115 · outbound

This paper cites Deep learning for universal linear embeddings of nonlinear dynamics.

Adversarial Autoencoders in Operator Learning Deep learning for universal linear embeddings of nonlinear dynamics

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.017635Z

Source-reported events for the cited work

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Observation ed3c6b6d-7b2e-4949-9a52-2fedd455b07f · outbound

This paper cites A survey on the methods and results of data-driven koopman analysis in the visualization of dynamical systems.

Adversarial Autoencoders in Operator Learning A survey on the methods and results of data-driven koopman analysis in the visualization of dynamical systems

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.009518Z

Source-reported events for the cited work

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Observation d4903b23-6bb8-4b02-96cd-7b5b3904543a · outbound

This paper cites Learning data-driven stable Koopman operators.

Adversarial Autoencoders in Operator Learning Learning data-driven stable Koopman operators

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:06.000717Z

Source-reported events for the cited work

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Observation b69d0cac-278a-48b3-ba25-5553156e61d7 · outbound

This paper cites Data-driven nonlinear stabilization using koop- man operator.

Adversarial Autoencoders in Operator Learning Data-driven nonlinear stabilization using koop- man operator

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.992504Z

Source-reported events for the cited work

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Observation 23ed5ef1-3e11-4f1e-8ecc-d438cc14c54c · outbound

This paper cites Data-driven approximation of the Koopman generator: Model reduc- tion, system identification, and control.

Adversarial Autoencoders in Operator Learning Data-driven approximation of the Koopman generator: Model reduc- tion, system identification, and control

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.984172Z

Source-reported events for the cited work

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Observation b8c544ca-0762-4838-91de-0acc6b651cbb · outbound

This paper cites Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control.

Adversarial Autoencoders in Operator Learning Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.975753Z

Source-reported events for the cited work

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Observation 12b2fc4f-ff57-4468-8256-ede790fd68cc · outbound

This paper cites Applied koopmanism.

Adversarial Autoencoders in Operator Learning Applied koopmanism

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.967381Z

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Observation 5a7fe72c-e703-4d1d-888d-f83fd95b0544 · outbound

This paper cites Multiresolution dynamic mode decomposi- tion.

Adversarial Autoencoders in Operator Learning Multiresolution dynamic mode decomposi- tion

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.958734Z

Source-reported events for the cited work

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Observation 8bc50d2d-0859-469f-9c87-91f55c8e85b8 · outbound

This paper cites Learning Koopman invariant sub- spaces for dynamic mode decomposition.

Adversarial Autoencoders in Operator Learning Learning Koopman invariant sub- spaces for dynamic mode decomposition

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.950620Z

Source-reported events for the cited work

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Observation 577d4d27-4a9f-4467-8503-e04ec30e6ece · outbound

This paper cites Koopman-mode decomposition of the cylinder wake.

Adversarial Autoencoders in Operator Learning Koopman-mode decomposition of the cylinder wake

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.942073Z

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Observation 436c9828-3d1a-46de-81c5-a6b7ff6ba2c1 · outbound

This paper cites an unresolved cited work.

Adversarial Autoencoders in Operator Learning Unresolved cited work

Reference 26

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Observation 6077f93c-a706-432f-8b03-c3f95131718b · outbound

This paper cites Learning Compositional Koopman Operators for Model-Based Control.

Adversarial Autoencoders in Operator Learning Learning Compositional Koopman Operators for Model-Based Control

Reference 27

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Observation 490435df-4446-4360-a9a1-4a3f6e740c2e · outbound

This paper cites Data-driven approximations of dy- namical systems operators for control.

Adversarial Autoencoders in Operator Learning Data-driven approximations of dy- namical systems operators for control

Reference 28

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Source-reported events for the cited work

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Observation 2885184c-d2e0-43b3-bb2d-28b0646588c4 · outbound

This paper cites Deep learning of Koopman representation for control.

Adversarial Autoencoders in Operator Learning Deep learning of Koopman representation for control

Reference 29

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Source-reported events for the cited work

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Observation 80fdc938-771b-4796-a63c-198523feca5a · outbound

This paper cites Koopman-based control of a soft continuum manipulator under variable loading conditions.

Adversarial Autoencoders in Operator Learning Koopman-based control of a soft continuum manipulator under variable loading conditions

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.907670Z

Source-reported events for the cited work

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Observation 9e3d11c2-bac2-4eb2-91b2-3450dbba8e44 · outbound

This paper cites Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control.

Adversarial Autoencoders in Operator Learning Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control

Reference 31

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Source-reported events for the cited work

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Observation 84eb3023-17d2-4b68-b1ad-418457629803 · outbound

This paper cites A data-driven koopman model predictive control framework for nonlinear partial differential equations.

Adversarial Autoencoders in Operator Learning A data-driven koopman model predictive control framework for nonlinear partial differential equations

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.899003Z

Source-reported events for the cited work

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Observation 318c6c05-918c-486a-a982-9bf4b8256e1b · outbound

This paper cites Model-Based Control Using Koopman Operators.

Adversarial Autoencoders in Operator Learning Model-Based Control Using Koopman Operators

Reference 33

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Source-reported events for the cited work

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Observation 484e93f1-82d4-49f5-899f-204d8d802cf9 · outbound

This paper cites Hamiltonian systems and transformation in Hilbert space.

Adversarial Autoencoders in Operator Learning Hamiltonian systems and transformation in Hilbert space

Reference 34

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b0bd82af-0082-4dff-8762-566d2be5a1d4 · outbound

This paper cites Modern Koopman Theory for Dynamical Systems.

Adversarial Autoencoders in Operator Learning Modern Koopman Theory for Dynamical Systems

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T19:07:05.582994Z

Source-reported events for the cited work

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Observation edf001eb-0c98-4b5e-8445-a504704831e2 · outbound

This paper cites What is the Koopman operator? a simplified treatment for discrete-time systems.

Adversarial Autoencoders in Operator Learning What is the Koopman operator? a simplified treatment for discrete-time systems

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.880804Z

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Observation 95dc980c-a941-4bc7-a864-193ec20ff5d5 · outbound

This paper cites Understanding quantum physics: A user’s manual.

Adversarial Autoencoders in Operator Learning Understanding quantum physics: A user’s manual

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.872019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 67d4c6ad-9929-48e1-9440-10834e1e3197 · outbound

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Adversarial Autoencoders in Operator Learning Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-11T19:07:05.862997Z

Source-reported events for the cited work

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Observation 18d5b481-3472-4f12-91cc-275ae65b73cf · outbound

This paper cites Griffiths.

Adversarial Autoencoders in Operator Learning Griffiths

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.854295Z

Source-reported events for the cited work

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Observation df79abd9-8275-4187-804f-85c32d02b56d · outbound

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Adversarial Autoencoders in Operator Learning Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-11T19:07:05.845266Z

Source-reported events for the cited work

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Observation 5ea4cea6-acf2-4b97-8db9-7e1c54885738 · outbound

This paper cites Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems.

Adversarial Autoencoders in Operator Learning Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-11T19:07:05.603724Z

Source-reported events for the cited work

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Observation 633cb381-71ba-4c0a-9c1e-4b6bff4f9460 · outbound

This paper cites A hierarchy of low-dimensional models for the transient and post- transient cylinder wake.

Adversarial Autoencoders in Operator Learning A hierarchy of low-dimensional models for the transient and post- transient cylinder wake

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.831330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5c547ec1-20ce-4763-a120-24744b29f902 · outbound

This paper cites an unresolved cited work.

Adversarial Autoencoders in Operator Learning Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-11T19:07:05.609333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08cb02f7-d7c9-4e9f-a5d1-400e39b9cd96 · outbound

This paper cites Interaction of “solitons.

Adversarial Autoencoders in Operator Learning Interaction of “solitons

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.816333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation eadbe861-062c-4263-ad13-776a57733430 · outbound

This paper cites Some Best Practices in Operator Learning.

Adversarial Autoencoders in Operator Learning Some Best Practices in Operator Learning

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-08-11T19:07:05.670351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 09720617-c91f-4caa-8e5d-3cd04fca43cc · outbound

This paper cites Automatic differentiation in PyTorch.

Adversarial Autoencoders in Operator Learning Automatic differentiation in PyTorch

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.806778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 16635bbb-4484-47e7-ae54-c70ccfadbcd0 · outbound

This paper cites Programming pytorch for deep learning: Creating and deploying deep learning applications.

Adversarial Autoencoders in Operator Learning Programming pytorch for deep learning: Creating and deploying deep learning applications

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.796392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9e9fed8c-5f6a-4bef-9d80-084bd1b53c75 · outbound

This paper cites UvA Deep Learning Tutorials.

Adversarial Autoencoders in Operator Learning UvA Deep Learning Tutorials

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.786765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation eb386cd3-36de-483d-8255-aa0b110af0d3 · outbound

This paper cites url: https://github.com/Lightning-AI/pytorch-lightning.

Adversarial Autoencoders in Operator Learning url: https://github.com/Lightning-AI/pytorch-lightning

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.777608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 34c7a06a-037f-4060-84ac-38ae5d3e5b5e · outbound

This paper cites Hydra - A framework for elegantly configuring complex applications.

Adversarial Autoencoders in Operator Learning Hydra - A framework for elegantly configuring complex applications

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:07:05.768565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5c63d6be-5379-47dd-8da1-6c4e89381f70 · outbound

This paper cites an unresolved cited work.

Adversarial Autoencoders in Operator Learning Unresolved cited work

Reference 2019

Resolution: unresolved; raw_fallback, observed 2026-08-11T19:07:05.759405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 40ade2c2-8611-46ed-9cc8-a60538a954d9 · outbound

This paper cites Loss Terms and Operator Forms of Koopman Autoencoders.

Adversarial Autoencoders in Operator Learning Loss Terms and Operator Forms of Koopman Autoencoders

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T19:07:05.600534Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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