Paper Citation Record · LEDGER

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

As of 17 August 2026, this Paper Citation Record lists 100 of 122 outbound references and 5 inbound Pith citation observations for arXiv:2506.10973.

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

pith.paper-citation-record.v1
2506.10973 v1

Coverage vector

measured 100 of 122 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:19:45.941582Z

measured 105 of 105 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T22:38:14.760597Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T00:07:27.763104Z

Reference resolution

100 of 122 outbound references displayed

verified exact7
verified fuzzy6
unresolved86
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 00dd4194-410f-4427-94a8-3762b4fdd2ca · outbound

This paper cites Graph Neural Operators for Classification of Spatial Transcriptomics Data.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Graph Neural Operators for Classification of Spatial Transcriptomics Data

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:19:50.648401Z

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Observation 8820b2f7-f360-4e4f-8063-02c3d3fb8dee · outbound

This paper cites Scalable Second Order Optimization for Deep Learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Scalable Second Order Optimization for Deep Learning

Reference 2

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Observation 4dd21b7b-e913-47bb-a82b-2682c4951099 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Neural operators for accelerating scientific simulations and design

Reference 3

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Observation d99d98bd-4940-4942-a755-febadd96a618 · outbound

This paper cites Neural Machine Translation by Jointly Learning to Align and Translate.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Neural Machine Translation by Jointly Learning to Align and Translate

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.157228Z

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Observation cb5e38cd-29f3-4381-8566-147f60a8226a · outbound

This paper cites Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:19:50.601515Z

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Observation ba8efcc7-f0e6-4237-a830-61b87449c9ac · outbound

This paper cites Model reduction and neural networks for parametric PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Model reduction and neural networks for parametric PDEs

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.309987Z

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Observation d6b2d32a-e8d0-435c-83d9-ac0e8019d626 · outbound

This paper cites Spherical Fourier neural operators: learning stable dynamics on the sphere.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Spherical Fourier neural operators: learning stable dynamics on the sphere

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.418641Z

Source-reported events for the cited work

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Observation 67e222c7-ad40-4e5f-b3df-2ef45cbbdbb6 · outbound

This paper cites A Mathematical Guide to Operator Learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning A Mathematical Guide to Operator Learning

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.504618Z

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Observation a9ae3cdf-820a-4f9b-9466-d996c3bb3f49 · outbound

This paper cites Lie point symmetry data augmentation for neural PDE solvers.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Lie point symmetry data augmentation for neural PDE solvers

Reference 9

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Observation 3447aa2a-6a76-4185-be88-5098445c4146 · outbound

This paper cites Message Passing Neural PDE Solvers.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Message Passing Neural PDE Solvers

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.643430Z

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Observation 18e57f7b-5bb5-4f61-aa7b-9cac3a344ace · outbound

This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.692994Z

Source-reported events for the cited work

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Observation eb5ee312-1bce-44b3-9f15-75d3b7ad338b · outbound

This paper cites Continuum attention for neural operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Continuum attention for neural operators

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.848083Z

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Observation bf8143b8-e235-41b6-aed1-905434b94a15 · outbound

This paper cites LNO: Laplace Neural Operator for Solving Differential Equations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning LNO: Laplace Neural Operator for Solving Differential Equations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:37.970292Z

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Observation 23d07326-9010-42a0-b535-a8b784d2795f · outbound

This paper cites Choose a transformer: Fourier or Galerkin.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Choose a transformer: Fourier or Galerkin

Reference 14

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Observation cda3e721-a224-46bb-8608-76fe3ddc0903 · outbound

This paper cites Neural operator surrogate models of plasma edge simulations: feasibility and data efficiency.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Neural operator surrogate models of plasma edge simulations: feasibility and data efficiency

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.159079Z

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Observation 780c0899-945e-4022-aaf9-4fb817214e30 · outbound

This paper cites Fourier Neural Operator based surrogates for $CO_2$ storage in realistic geologies.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Fourier Neural Operator based surrogates for $CO_2$ storage in realistic geologies

Reference 16

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T04:19:50.316146Z

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Observation 25db135b-d0df-46e5-8be8-70eddb11b500 · outbound

This paper cites CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.291069Z

Source-reported events for the cited work

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Observation 64d9de40-2e1a-4e5a-80cb-d46c4f194e60 · outbound

This paper cites Equivariant neural operator learning with graphon convolution.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Equivariant neural operator learning with graphon convolution

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.349184Z

Source-reported events for the cited work

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Observation 9f3ead40-6f32-4eda-a301-f5230cc148b8 · outbound

This paper cites Rethinking Attention with Performers.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Rethinking Attention with Performers

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.460653Z

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Observation 360afbbf-882c-4f6b-bb40-a4085b9c079c · outbound

This paper cites Fourier neural operator for fluid flow in small-shape 2D simulated porous media dataset.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Fourier neural operator for fluid flow in small-shape 2D simulated porous media dataset

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.567589Z

Source-reported events for the cited work

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Observation d497ef5e-2392-4f4d-b012-3a04ed98655c · outbound

This paper cites Neural Operator Learning for Ultrasound Tomography Inversion.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Neural Operator Learning for Ultrasound Tomography Inversion

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.746305Z

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Observation 1a11a305-64ad-46c6-ad0b-8cfbd03d05a2 · outbound

This paper cites Generic bounds on the approximation error for physics-informed (and) operator learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Generic bounds on the approximation error for physics-informed (and) operator learning

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.811713Z

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Observation ed7bba38-0b61-4c0b-a00c-96f8eab62671 · outbound

This paper cites Nonlinear approximation.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Nonlinear approximation

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:38.919015Z

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Observation e0c857ca-aed7-4e43-848a-95a8e61114ba · outbound

This paper cites An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:39.073853Z

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Observation 0c05ad68-09d0-4d78-af96-468664df8933 · outbound

This paper cites an unresolved cited work.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Unresolved cited work

Reference 25

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Observation b68c64f1-bd3c-493c-97a7-4cca2749d8a0 · outbound

This paper cites Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEs

Reference 26

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Observation 12ab5168-fedb-4a35-b232-7d0fbbb96e5e · outbound

This paper cites Understanding the difficulty of training deep feedforward neural networks.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Understanding the difficulty of training deep feedforward neural networks

Reference 27

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Observation 7121deef-1fcf-4a0d-a472-d7e4d22981f1 · outbound

This paper cites A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Reference 28

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Observation bf1d390f-9987-432e-b711-ba6ca25ba086 · outbound

This paper cites Plasma surrogate modelling using fourier neural operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Plasma surrogate modelling using fourier neural operators

Reference 29

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Observation 919b661d-c03b-4f7c-b2ee-7816d9aa21f7 · outbound

This paper cites Theory-to-Practice Gap for Neural Networks and Neural Operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Theory-to-Practice Gap for Neural Networks and Neural Operators

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:19:49.779408Z

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Observation 0443064e-9a31-4a38-a341-99560acfe117 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

Reference 31

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Observation d60acc77-b6da-4265-95e0-143e1c8cc669 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Multiwavelet-based operator learning for differential equations

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:39.678160Z

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Observation c85b6baf-d111-4190-8b64-5dfa33a66773 · outbound

This paper cites Towards Multi-spatiotemporal-scale Generalized PDE Modeling.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 33

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Observation dca77ab1-f27d-4957-aabe-69e146cacfc1 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning GNOT : A general neural operator transformer for operator learning

Reference 34

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This paper cites PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs

Reference 35

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Observation 268bae01-c943-41ac-8fbd-7d9c9b77844b · outbound

This paper cites DPOT : Auto-regressive denoising operator transformer for large-scale PDE pre-training.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning DPOT : Auto-regressive denoising operator transformer for large-scale PDE pre-training

Reference 36

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This paper cites Delving deep into rectifiers: Surpassing human-level performance on imagenet classification.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Delving deep into rectifiers: Surpassing human-level performance on imagenet classification

Reference 37

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This paper cites Group Equivariant Fourier Neural Operators for Partial Differential Equations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Group Equivariant Fourier Neural Operators for Partial Differential Equations

Reference 38

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This paper cites Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Reference 39

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This paper cites A Unified Model for Compressed Sensing MRI Across Undersampling Patterns.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning A Unified Model for Compressed Sensing MRI Across Undersampling Patterns

Reference 40

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Observation f112dd92-d1c4-465f-aa1f-724d84036006 · outbound

This paper cites Perfception: Perception using radiance fields.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Perfception: Perception using radiance fields

Reference 41

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This paper cites Jiang, Z.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Jiang, Z

Reference 42

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Observation 41473fc8-52c1-4bc2-bc45-d089d3e4b65b · outbound

This paper cites Resolution-invariant image classification based on Fourier neural operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Resolution-invariant image classification based on Fourier neural operators

Reference 43

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This paper cites Multi-task learning using uncertainty to weigh losses for scene geometry and semantics.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Multi-task learning using uncertainty to weigh losses for scene geometry and semantics

Reference 44

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This paper cites Adam: A Method for Stochastic Optimization.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Adam: A Method for Stochastic Optimization

Reference 45

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This paper cites Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs

Reference 46

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This paper cites A library for learning neural operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning A library for learning neural operators

Reference 47

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning On universal approximation and error bounds for Fourier neural operators

Reference 48

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This paper cites Neural operator: Learning maps between function spaces with applications to PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Neural operator: Learning maps between function spaces with applications to PDEs

Reference 49

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Observation 2d0dcf55-f5c7-4454-b08c-9947d0646a16 · outbound

This paper cites Data Complexity Estimates for Operator Learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Data Complexity Estimates for Operator Learning

Reference 50

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Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Operator Learning: Algorithms and Analysis

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.203654Z

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This paper cites FourCastNet : Accelerating global high-resolution weather forecasting using adaptive Fourier neural operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning FourCastNet : Accelerating global high-resolution weather forecasting using adaptive Fourier neural operators

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.277479Z

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This paper cites Artificial neural networks for solving ordinary and partial differential equations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Artificial neural networks for solving ordinary and partial differential equations

Reference 53

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Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Learning skillful medium-range global weather forecasting

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.490060Z

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This paper cites Operator learning with PCA-Net: upper and lower complexity bounds.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Operator learning with PCA-Net: upper and lower complexity bounds

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.578374Z

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Error estimates for DeepONets : A deep learning framework in infinite dimensions

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.685118Z

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Observation cfe36226-36bd-4af7-a4f3-219c176919a1 · outbound

This paper cites Nonlocality and Nonlinearity Implies Universality in Operator Learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Nonlocality and Nonlinearity Implies Universality in Operator Learning

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.783966Z

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Observation 4b20f443-e8d0-4e8e-8312-775e66b04d04 · outbound

This paper cites Discretization error of Fourier neural operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Discretization error of Fourier neural operators

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.871510Z

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This paper cites Layer normalization.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Layer normalization

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:41.968316Z

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Observation c11539d3-a14c-415f-b1dd-ca1092fedbc3 · outbound

This paper cites Fourier neural operator approach to large eddy simulation of three-dimensional turbulence.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Fourier neural operator approach to large eddy simulation of three-dimensional turbulence

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.116875Z

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Observation ae24f956-d4e9-4767-8601-7bcc46c153d1 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Transformer for Partial Differential Equations' Operator Learning

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.212865Z

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Observation bff56065-a708-4ba4-9822-3198142a3994 · outbound

This paper cites Scalable transformer for PDE surrogate modeling.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Scalable transformer for PDE surrogate modeling

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.351681Z

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Observation 2e97d5a9-245e-4e9e-a826-da10601e3ba1 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Fourier Neural Operator for Parametric Partial Differential Equations

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.459126Z

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Observation 14683edc-eb1a-4537-9a29-452c18c610f1 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.568678Z

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Observation 6af54edf-9ddb-45e9-85f1-f501807d6c4f · outbound

This paper cites Multipole graph neural operator for parametric partial differential equations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Multipole graph neural operator for parametric partial differential equations

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.654444Z

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Observation 51950819-d9db-4638-8c08-08cec04efb93 · outbound

This paper cites Learning chaotic dynamics in dissipative systems.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Learning chaotic dynamics in dissipative systems

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.739063Z

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Observation a3a25da1-bcaa-493b-9a81-8abb65fd1e00 · outbound

This paper cites Fourier neural operator with learned deformations for PDEs on general geometries.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Fourier neural operator with learned deformations for PDEs on general geometries

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.867385Z

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Observation 95c5aadb-b5a3-4200-a122-9714eb52b208 · outbound

This paper cites Geometry-informed neural operator for large-scale 3d PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Geometry-informed neural operator for large-scale 3d PDEs

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:42.951234Z

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Observation 04fd670f-7dfc-4ec7-afa1-ba44f2a130d3 · outbound

This paper cites Physics-informed neural operator for learning partial differential equations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Physics-informed neural operator for learning partial differential equations

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.034448Z

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Observation 4abb3cad-0d51-422e-a637-66342bc8bdc8 · outbound

This paper cites Graph metanetworks for processing diverse neural architectures.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Graph metanetworks for processing diverse neural architectures

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.082239Z

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Observation f4aad941-a27b-4e42-b288-b4650c6fb6e3 · outbound

This paper cites Lin, Julius Berner, Valentin Duruisseaux, David Pitt, Daniel Leibovici, Jean Kossaifi, Kamyar Azizzadenesheli, and Anima Anandkumar.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Lin, Julius Berner, Valentin Duruisseaux, David Pitt, Daniel Leibovici, Jean Kossaifi, Kamyar Azizzadenesheli, and Anima Anandkumar

Reference 71

Resolution: verified exact; raw_fallback, observed 2026-08-07T04:19:49.010047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 56abb7e4-e101-4aa2-bbe8-670cdb9a20ff · outbound

This paper cites Beyond regular grids: Fourier -based neural operators on arbitrary domains.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Beyond regular grids: Fourier -based neural operators on arbitrary domains

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.250454Z

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Observation bc4f0a2e-209a-4a2f-84fe-6cbbfb5f77ad · outbound

This paper cites Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.335110Z

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Observation 00fe4614-b87c-456f-9d5e-925c733ad8b4 · outbound

This paper cites Neural Operators with Localized Integral and Differential Kernels.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Neural Operators with Localized Integral and Differential Kernels

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.434997Z

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Observation 064a9a30-a109-41b9-b213-5cb0d00adfb4 · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.523729Z

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Observation 34e7bec4-d7fe-410f-9bee-f3a5e6820bb4 · outbound

This paper cites Effective Approaches to Attention-based Neural Machine Translation.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Effective Approaches to Attention-based Neural Machine Translation

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.629177Z

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Observation 5d2a7770-08e1-4ce3-9a58-0f4f4dc3a721 · outbound

This paper cites Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.722191Z

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Observation 07a668fa-5a26-4a92-b320-52f0607b8d27 · outbound

This paper cites Fourier continuation for exact derivative computation in physics-informed neural operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Fourier continuation for exact derivative computation in physics-informed neural operators

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.834054Z

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Observation ae1b6fe4-0bd9-49b6-b087-e100cd9c8feb · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning NeRF : Representing scenes as neural radiance fields for view synthesis

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.892178Z

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Observation c09cae4c-612b-4d67-b945-061028dc9bfe · outbound

This paper cites Position: Optimization in SciML should employ the function space geometry.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Position: Optimization in SciML should employ the function space geometry

Reference 80

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:43.973455Z

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Observation 85ea898d-c151-485b-9a14-3edc40b35b46 · outbound

This paper cites Instant neural graphics primitives with a multiresolution hash encoding.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Instant neural graphics primitives with a multiresolution hash encoding

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.107088Z

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Observation 4e58b1c9-edb9-4361-8155-3aebaf575abd · outbound

This paper cites The well: a large-scale collection of diverse physics simulations for machine learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning The well: a large-scale collection of diverse physics simulations for machine learning

Reference 82

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.189035Z

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Observation 2583b7c8-cd2f-4eab-bdf8-fe6683913079 · outbound

This paper cites Pamela, N.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Pamela, N

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.270107Z

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Observation 04a7e6db-c228-4242-a1c4-accbf82d126a · outbound

This paper cites Robust Confinement State Classification with Uncertainty Quantification through Ensembled Data-Driven Methods.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Robust Confinement State Classification with Uncertainty Quantification through Ensembled Data-Driven Methods

Reference 84

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:19:48.604436Z

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Observation d7e9a9ae-cc13-43bb-bf8a-72ab38486892 · outbound

This paper cites Generative Adversarial Neural Operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Generative Adversarial Neural Operators

Reference 85

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.445827Z

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Observation d4afae23-70d0-4564-b2e3-5aee71094830 · outbound

This paper cites U-NO: U-shaped Neural Operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning U-NO: U-shaped Neural Operators

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.552852Z

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Observation d6346b51-4a65-49ea-9417-20bd0ffd16e7 · outbound

This paper cites Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs

Reference 87

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.728299Z

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Observation 786668ef-c95b-4c37-9205-a43927880722 · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 88

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.814455Z

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Observation c09c71a1-f94a-461c-80a4-b5e3518c0e1c · outbound

This paper cites Convolutional neural operators for robust and accurate learning of PDEs.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Convolutional neural operators for robust and accurate learning of PDEs

Reference 89

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:44.921368Z

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Observation 0157c5c8-4d8c-432e-bb87-572163becff1 · outbound

This paper cites Anoop Krishnan.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Anoop Krishnan

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:19:50.890799Z

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Observation 266e8ba4-2deb-4abf-855b-4e5155f4ea37 · outbound

This paper cites An introduction to partial differential equations, volume 13.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning An introduction to partial differential equations, volume 13

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:19:50.875936Z

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Observation 62edbec5-9427-4a41-8530-661ff3aeb2df · outbound

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

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning U-Net : Convolutional networks for biomedical image segmentation

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:19:50.859601Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2209e17e-fd87-4364-bdac-443f5bdfb271 · outbound

This paper cites NOMAD : Nonlinear manifold decoders for operator learning.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning NOMAD : Nonlinear manifold decoders for operator learning

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:19:50.845558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 93d0ff59-98f7-4d69-9743-951e65355fa7 · outbound

This paper cites Variational Autoencoding Neural Operators.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Variational Autoencoding Neural Operators

Reference 94

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:45.408265Z

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Observation eb227f67-eed9-400b-a099-381bd1cf9767 · outbound

This paper cites Operator Learning with Neural Fields: Tackling PDEs on General Geometries.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Operator Learning with Neural Fields: Tackling PDEs on General Geometries

Reference 95

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:19:48.391421Z

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Observation 9876bc7a-6122-467a-a5ee-7a403aaaa61a · outbound

This paper cites Parallel physics-informed neural networks via domain decomposition.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Parallel physics-informed neural networks via domain decomposition

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:19:50.831543Z

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Observation 6042346f-df2c-411c-a16f-72ff7c78275c · outbound

This paper cites DGM : A deep learning algorithm for solving partial differential equations.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning DGM : A deep learning algorithm for solving partial differential equations

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:19:50.817427Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation acc6d6be-9a03-4b3f-b496-0937b6ab3c7c · outbound

This paper cites Implicit neural representations with periodic activation functions.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Implicit neural representations with periodic activation functions

Reference 98

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:45.756425Z

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Observation 3ab5da72-07a1-4dbb-b53a-7ecd8049a173 · outbound

This paper cites RoFormer : Enhanced transformer with rotary position embedding.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning RoFormer : Enhanced transformer with rotary position embedding

Reference 99

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:45.852175Z

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Observation 964046dc-c07f-4b72-9727-8ce948b70d39 · outbound

This paper cites Operator Learning: A Statistical Perspective.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Operator Learning: A Statistical Perspective

Reference 100

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:45.941582Z

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Pith citing papers

Observation 5817f286-feff-4915-9278-711bfe050c9b · inbound

Learning Neural Operator Surrogates for the Black Hole Accretion Code cites this paper.

Learning Neural Operator Surrogates for the Black Hole Accretion Code Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

Reference 49

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:21:23.410159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 97ff7466-23e3-4c46-9b57-5b014265e303 · inbound

Limits of Resolution Equivariance in Fourier Neural Operators cites this paper.

Limits of Resolution Equivariance in Fourier Neural Operators Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T19:32:34.956583Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c0dbacd4-b016-4e6d-8fb8-4dbf67ada3a1 · inbound

Evaluating Operators for Acoustic Wave Simulation Correction cites this paper.

Evaluating Operators for Acoustic Wave Simulation Correction Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

Reference 22

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T00:07:27.764660Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 08f4bd3e-28c3-42f3-9acd-6212029f3a69 · inbound

Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs cites this paper.

Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T18:45:58.268142Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b9f19e1d-a630-4492-a403-9ae92b74562d · inbound

A neural operator view on U-Nets for inverse imaging problems cites this paper.

A neural operator view on U-Nets for inverse imaging problems Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T22:38:14.760597Z

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