Paper Citation Record · LEDGER

Some Best Practices in Operator Learning

As of 22 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 1 inbound Pith citation observation for arXiv:2412.06686.

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

pith.paper-citation-record.v1
2412.06686 v1

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measured 63 of 63 reference resolution

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measured 64 of 64 standing notices

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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Reference resolution

63 of 63 outbound references displayed

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External citation measurements

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Outbound references

Observation 19714859-d53c-44f8-b96c-82b5665322e7 · outbound

This paper cites Operator Learning: Algorithms and Analysis.

Some Best Practices in Operator Learning Operator Learning: Algorithms and Analysis

Reference 1

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Observation 9bfea1ed-eab3-40f4-9816-0db670ab75c0 · outbound

This paper cites A Mathematical Guide to Operator Learning.

Some Best Practices in Operator Learning A Mathematical Guide to Operator Learning

Reference 2

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Observation 324a73e2-0671-4f1b-9d9d-17ce7b18ef57 · outbound

This paper cites NeuralNetworkApproximationstoSolutionOperatorsforPartialDifferential Equations.

Some Best Practices in Operator Learning NeuralNetworkApproximationstoSolutionOperatorsforPartialDifferential Equations

Reference 3

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Observation e3a7742c-ff85-4029-9445-2caf3057242a · outbound

This paper cites LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators.

Some Best Practices in Operator Learning LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators

Reference 4

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Observation 2429b49a-6110-41dd-b6a8-a374d78b6b73 · outbound

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

Some Best Practices in Operator Learning Error estimates for deep- onets: A deep learning framework in infinite dimensions

Reference 5

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Observation 72db37e9-7ebd-44fd-95bc-d2b5a2d4cc0a · outbound

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

Some Best Practices in Operator Learning A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

Reference 6

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Observation e0401893-d788-4dcc-891b-0aa17c07f2c1 · outbound

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

Some Best Practices in Operator Learning Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads

Reference 7

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Observation 8b7645ca-7388-4e4a-a990-5a63522ec2d1 · outbound

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

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

Reference 8

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Source-reported events for the cited work

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Observation 95301666-2cd1-4953-8c00-5648caeee89f · outbound

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

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

Reference 9

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Observation e73a05e4-b456-4c3d-9370-d36cf33d80db · outbound

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

Some Best Practices in Operator Learning Fourier Neural Operator for Parametric Partial Differential Equations

Reference 10

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 275ed08c-56ec-46ea-9ceb-d70af5928cf0 · outbound

This paper cites Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective.

Some Best Practices in Operator Learning Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective

Reference 11

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Observation 01c8e021-958c-4ee1-b881-24ddb8751b35 · outbound

This paper cites Fourier neural operator with learned deformations for pdes on general ge- ometries.

Some Best Practices in Operator Learning Fourier neural operator with learned deformations for pdes on general ge- ometries

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:07.343545Z

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Observation 0ce2f1f6-14b0-4fae-b83e-57a836c6f9c1 · outbound

This paper cites Lie point symmetry data aug- mentation for neural PDE solvers.

Some Best Practices in Operator Learning Lie point symmetry data aug- mentation for neural PDE solvers

Reference 13

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Observation a24cf304-777d-4322-8a85-6add283dd2ff · outbound

This paper cites On universal approximation and error bounds for Fourier neural operators.

Some Best Practices in Operator Learning On universal approximation and error bounds for Fourier neural operators

Reference 14

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Observation ddcdea3e-0eb9-43ac-b1f0-4dbafe3815cc · outbound

This paper cites Factorized Fourier Neural Operators.

Some Best Practices in Operator Learning Factorized Fourier Neural Operators

Reference 15

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Observation 2def6e79-2adc-43d9-938e-efd159d5c70c · outbound

This paper cites Fourier features let networks learn high frequency functions in low di- mensionaldomains.

Some Best Practices in Operator Learning Fourier features let networks learn high frequency functions in low di- mensionaldomains

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:07.138011Z

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Observation 7d4542ea-ab51-4dbd-a553-ebeb08d68250 · outbound

This paper cites an unresolved cited work.

Some Best Practices in Operator Learning Unresolved cited work

Reference 17

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Observation 552417fb-1ef5-4c84-9b4d-57c56d256494 · outbound

This paper cites Springer Science & Business Media, 2011.

Some Best Practices in Operator Learning Springer Science & Business Media, 2011

Reference 18

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Observation 63a85d85-9769-4263-966f-9141ea704703 · outbound

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

Some Best Practices in Operator Learning Deep learning for universal linear embeddings of nonlinear dynamics

Reference 19

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Observation 118f7904-04db-455a-a007-7751ab13c457 · outbound

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

Some Best Practices in Operator Learning A survey on the methods and results of data-driven koopman analysis in the visualization of dynamical systems

Reference 20

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Observation 8bac7e47-e395-4702-9113-08d0dbe2c900 · outbound

This paper cites Learning data-driven stable Koopman operators.

Some Best Practices in Operator Learning Learning data-driven stable Koopman operators

Reference 21

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Observation 3f919f0b-2898-42c2-817a-df3f75199d8b · outbound

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

Some Best Practices in Operator Learning Data-driven nonlinear stabilization using koop- man operator

Reference 22

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Observation e710fb51-5b0c-495b-9965-0ce629ac5156 · outbound

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

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

Reference 23

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Observation 63e4610e-960e-4783-b80b-98856fbf2cb6 · outbound

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

Some Best Practices in Operator Learning Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control

Reference 24

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Observation b50a1e23-7cfc-4815-8de0-33c041c92245 · outbound

This paper cites Applied koopmanism.

Some Best Practices in Operator Learning Applied koopmanism

Reference 25

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Observation d2ecbbb1-eece-4bdd-8545-8c214cd392f5 · outbound

This paper cites Multiresolution dynamic mode decomposi- tion.

Some Best Practices in Operator Learning Multiresolution dynamic mode decomposi- tion

Reference 26

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Observation 2966dcf6-e345-43d9-8186-d7f616ba4c81 · outbound

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

Some Best Practices in Operator Learning Learning Koopman invariant sub- spaces for dynamic mode decomposition

Reference 27

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Observation 6ed72b34-f27e-42ed-b9be-2378ea2ae257 · outbound

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

Some Best Practices in Operator Learning Koopman-mode decomposition of the cylinder wake

Reference 28

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Observation 372904bf-e823-4336-858f-c07f1a8ccf7f · outbound

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Some Best Practices in Operator Learning Unresolved cited work

Reference 29

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Observation bb1625dd-dee9-4226-8ad1-4b7b6913c8cb · outbound

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

Some Best Practices in Operator Learning Learning Compositional Koopman Operators for Model-Based Control

Reference 30

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Observation d1065aa1-3d7f-43b6-8b07-89826832a2bc · outbound

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

Some Best Practices in Operator Learning Data-driven approximations of dy- namical systems operators for control

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:06.506922Z

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Observation e8018667-0d3c-44b0-8cd1-a3b25c1770b2 · outbound

This paper cites Deep learning of Koopman representation for control.

Some Best Practices in Operator Learning Deep learning of Koopman representation for control

Reference 32

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Observation 617ebff8-17c5-4783-b55a-3bd237c71e2b · outbound

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

Some Best Practices in Operator Learning Koopman-based control of a soft continuum manipulator under variable loading conditions

Reference 33

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Observation 85eec064-6498-4c38-8469-e7a1757facd5 · outbound

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

Some Best Practices in Operator Learning Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control

Reference 34

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Observation 50f92215-8ebe-4817-b779-19c8cff7da21 · outbound

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

Some Best Practices in Operator Learning A data-driven koopman model predictive control framework for nonlinear partial differential equations

Reference 35

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Observation 824c9b36-eae7-4479-b640-889b689d3891 · outbound

This paper cites Model-Based Control Using Koopman Operators.

Some Best Practices in Operator Learning Model-Based Control Using Koopman Operators

Reference 36

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Observation e0999240-0f40-4ff8-a825-eb67545d5ddc · outbound

This paper cites Hamiltonian systems and transformation in Hilbert space.

Some Best Practices in Operator Learning Hamiltonian systems and transformation in Hilbert space

Reference 37

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Observation 55c398a4-a217-422c-82c5-7a44516c91e8 · outbound

This paper cites Modern Koopman Theory for Dynamical Systems.

Some Best Practices in Operator Learning Modern Koopman Theory for Dynamical Systems

Reference 38

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Observation 404c7238-9e5e-486b-b104-f390b6a08e7d · outbound

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

Some Best Practices in Operator Learning What is the Koopman operator? a simplified treatment for discrete-time systems

Reference 39

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

Some Best Practices in Operator Learning Understanding quantum physics: A user’s manual

Reference 40

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Some Best Practices in Operator Learning Unresolved cited work

Reference 41

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Some Best Practices in Operator Learning Griffiths

Reference 42

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Some Best Practices in Operator Learning Unresolved cited work

Reference 43

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

Some Best Practices in Operator Learning Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems

Reference 44

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Observation d4c96ec2-11bd-40b5-b0b1-66803624fdea · outbound

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

Some Best Practices in Operator Learning A hierarchy of low-dimensional models for the transient and post- transient cylinder wake

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:06.059674Z

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Observation ad880e6f-d25a-44b5-8352-8c9cd955dcd4 · outbound

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Some Best Practices in Operator Learning Unresolved cited work

Reference 46

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This paper cites Interaction of “solitons.

Some Best Practices in Operator Learning Interaction of “solitons

Reference 47

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This paper cites Improving neural networks by preventing co-adaptation of feature detectors.

Some Best Practices in Operator Learning Improving neural networks by preventing co-adaptation of feature detectors

Reference 48

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This paper cites Dropout: a simple way to prevent neural networks from overfitting.

Some Best Practices in Operator Learning Dropout: a simple way to prevent neural networks from overfitting

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:05.867352Z

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Observation 26c0d834-e43b-4713-addd-8399a81c6b86 · outbound

This paper cites Averaging Weights Leads to Wider Optima and Better Generalization.

Some Best Practices in Operator Learning Averaging Weights Leads to Wider Optima and Better Generalization

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.639341Z

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Observation 36197c23-a3cf-4b06-8ab5-821ee4dd5eb7 · outbound

This paper cites There Are Many Consistent Explanations of Unlabeled Data: Why You Should Average.

Some Best Practices in Operator Learning There Are Many Consistent Explanations of Unlabeled Data: Why You Should Average

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.653620Z

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Observation 6f062a0f-6d80-431b-a741-e0e07f30dd78 · outbound

This paper cites Improving stability in deep reinforcement learning with weight av- eraging.

Some Best Practices in Operator Learning Improving stability in deep reinforcement learning with weight av- eraging

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:05.740763Z

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Observation 4c105ba0-ef84-4f0c-9cf7-588a5991e65a · outbound

This paper cites Accessed: October 2024.

Some Best Practices in Operator Learning Accessed: October 2024

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:05.679142Z

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Observation 2f612ad0-0268-4b21-884a-f6609dc2c2ff · outbound

This paper cites Cyclical learning rates for training neural networks.

Some Best Practices in Operator Learning Cyclical learning rates for training neural networks

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:24:05.642189Z

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Observation 355fd820-b7cc-4138-a443-29807ff5ffbf · outbound

This paper cites On the Variance of the Adaptive Learning Rate and Beyond.

Some Best Practices in Operator Learning On the Variance of the Adaptive Learning Rate and Beyond

Reference 55

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This paper cites A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation.

Some Best Practices in Operator Learning A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.721290Z

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Some Best Practices in Operator Learning Automatic differentiation in PyTorch

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.732638Z

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

Some Best Practices in Operator Learning Programming pytorch for deep learning: Creating and deploying deep learning applications

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.758585Z

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This paper cites UvA Deep Learning Tutorials.

Some Best Practices in Operator Learning UvA Deep Learning Tutorials

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.774291Z

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

Some Best Practices in Operator Learning url: https://github.com/Lightning-AI/pytorch-lightning

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.790239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a584710-87ca-417a-94d7-2ec4d179cf7e · outbound

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

Some Best Practices in Operator Learning Hydra - A framework for elegantly configuring complex applications

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.797361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a324030-2b2a-4a65-94d2-d34c0f982861 · outbound

This paper cites an unresolved cited work.

Some Best Practices in Operator Learning Unresolved cited work

Reference 2019

Resolution: unresolved; raw_fallback, observed 2026-08-11T19:24:05.237474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cb146f1e-f272-4cce-bb7b-e24128970e4b · outbound

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

Some Best Practices in Operator Learning Loss Terms and Operator Forms of Koopman Autoencoders

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.528996Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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

Adversarial Autoencoders in Operator Learning cites this paper.

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 2026-08-22T06:32:14.747728+00:00.