Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning | Paper Citation Record

Observation 69518dc7-eddc-401b-a576-6dda1e35a118 · outbound

This paper cites Fourcastnet: A global data- driven high-resolution weather model using adaptive fourier neural operators, 2022.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Fourcastnet: A global data- driven high-resolution weather model using adaptive fourier neural operators, 2022

Reference 1

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Observation 5c9febae-ed77-4fa9-9001-c4f98bf3a752 · outbound

This paper cites Spherical fourier neural operators: learning stable dynam- ics on the sphere.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Spherical fourier neural operators: learning stable dynam- ics on the sphere

Reference 2

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Observation 8fb5a243-d739-4f79-9d5c-1a43a4aefc70 · outbound

This paper cites Fourier neural operator for parametric partial differen- tial equations, 2021.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Fourier neural operator for parametric partial differen- tial equations, 2021

Reference 3

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Observation fbe30cde-0e84-4712-bf8d-102815c353a2 · outbound

This paper cites Yeh, Jean Kossaifi, Kamyar Azizzade- nesheli, and Anima Anandkumar.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Yeh, Jean Kossaifi, Kamyar Azizzade- nesheli, and Anima Anandkumar

Reference 4

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Observation 8cc1a9ff-76f6-4c08-b34b-e55121726db3 · outbound

This paper cites Fourier neural operator for plasma modelling, 2023.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Fourier neural operator for plasma modelling, 2023

Reference 5

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Observation d03e0528-9ebb-42e0-bfc5-782ebc37e96e · outbound

This paper cites Carey, L.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Carey, L

Reference 6

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Observation 56e94fac-3390-41f5-826f-98564468d2a6 · outbound

This paper cites Khorrami, Pawan Goyal, Jaber R.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Khorrami, Pawan Goyal, Jaber R

Reference 7

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Observation aa05da7a-63dd-4e4f-b854-3927ba2bb5f9 · outbound

This paper cites A neural operator based hybrid microscale model for multiscale simulation of rate-dependent materials, 2025.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning A neural operator based hybrid microscale model for multiscale simulation of rate-dependent materials, 2025

Reference 8

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Observation 4777f059-0338-49e2-a5c0-60df0d456c93 · outbound

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

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Fourier neural operator with learned deformations for pdes on general geometries.J

Reference 9

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Observation 32bf955f-ab6a-4d02-9c89-1d6d8213bdc7 · outbound

This paper cites Transolver: A fast transformer solver for pdes on general geometries, 2024.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Transolver: A fast transformer solver for pdes on general geometries, 2024

Reference 10

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Observation 5f979f4f-1555-494c-9950-94cb191342c0 · outbound

This paper cites Transolver++: An accurate neural solver for pdes on million-scale geometries, 2025.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Transolver++: An accurate neural solver for pdes on million-scale geometries, 2025

Reference 11

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Observation a3cb6946-2abc-4163-85af-106a78defe34 · outbound

This paper cites Transolver-3: Scaling up transformer solvers to industrial-scale geometries, 2026.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Transolver-3: Scaling up transformer solvers to industrial-scale geometries, 2026

Reference 12

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Observation fb3f249b-0422-475b-94da-3e52a86f0c50 · outbound

This paper cites Chandra Mouli, Danielle C.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Chandra Mouli, Danielle C

Reference 13

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Observation 840c9c18-be51-4503-9780-cde61a49325b · outbound

This paper cites Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis

Reference 14

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Observation c77519cd-3f93-49eb-81a9-4ba0d6e7783a · outbound

This paper cites Active learning for neural PDE solvers.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Active learning for neural PDE solvers

Reference 15

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Observation 290d3af1-5021-440f-a6d5-a2b48dec8375 · outbound

This paper cites Simple and scalable predictive uncertainty estimation using deep ensembles.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Simple and scalable predictive uncertainty estimation using deep ensembles

Reference 16

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Observation 5eafb7b4-d652-4399-bab9-b0d628103e83 · outbound

This paper cites Dropout as a bayesian approximation: representing model uncertainty in deep learning.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Dropout as a bayesian approximation: representing model uncertainty in deep learning

Reference 17

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Observation aea366e3-9123-447b-b15a-dd0b2a5fcea4 · outbound

This paper cites Light-weight diffusion multiplier and uncertainty quantification for fourier neural operators, 2025.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Light-weight diffusion multiplier and uncertainty quantification for fourier neural operators, 2025

Reference 18

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Observation 78b24af4-a889-47e3-be6f-131bc0b5d3c9 · outbound

This paper cites Laplace redux - effortless bayesian deep learning.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Laplace redux - effortless bayesian deep learning

Reference 19

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Observation c5f54a56-c9cb-4a8b-9c5a-e820513e0847 · outbound

This paper cites Linearization turns neural operators into function-valued gaussian processes.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Linearization turns neural operators into function-valued gaussian processes

Reference 20

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Observation e7345766-9fa1-44be-b0cb-a442537d8865 · outbound

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Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Unresolved cited work

Reference 21

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Observation 2e230248-4693-426a-8eb2-2beb174f9e9b · outbound

This paper cites Operator learning with gaussian processes.Computer Methods in Applied Mechanics and Engineering, 434:117581, 2025.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Operator learning with gaussian processes.Computer Methods in Applied Mechanics and Engineering, 434:117581, 2025

Reference 22

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Observation a4ea13a4-b4c8-4c1c-be08-b8bc57a7a783 · outbound

This paper cites Kernel methods are competitive for operator learning.Journal of Computational Physics, 496, 2024.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Kernel methods are competitive for operator learning.Journal of Computational Physics, 496, 2024

Reference 23

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Observation 73ad8316-fa8e-45c6-984e-decdb877818e · outbound

This paper cites Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-07-03T20:08:55.690340Z

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Observation 0da2da73-c066-4c65-aee4-981ed78e92ea · outbound

This paper cites Error analysis of kernel/gp methods for nonlinear and parametric pdes.Journal of Computational Physics, 520:113488, 2025.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Error analysis of kernel/gp methods for nonlinear and parametric pdes.Journal of Computational Physics, 520:113488, 2025

Reference 25

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Observation ff5f01cf-bb1a-41d4-88ff-c4251eacfde5 · outbound

This paper cites On the brittleness of bayesian inference.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning On the brittleness of bayesian inference

Reference 26

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Observation aceca5e2-bf00-49c7-b9f5-1f167b8dfa53 · outbound

This paper cites Kernel flows: From learning kernels from data into the abyss.Journal of Computational Physics, 389:22–47, 2019.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Kernel flows: From learning kernels from data into the abyss.Journal of Computational Physics, 389:22–47, 2019

Reference 27

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Observation b14b4249-c57c-4490-a811-e8b1f4c9578d · outbound

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

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Geometry-informed neural operator for large-scale 3d PDEs

Reference 28

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Observation 6a501367-c7ed-4eb2-9b63-479c3ee01ee7 · outbound

This paper cites Kernel interpolation for scalable structured gaussian processes (kiss-gp).

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Kernel interpolation for scalable structured gaussian processes (kiss-gp)

Reference 29

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Observation 1d5be437-cba5-4d0c-ab2f-cdde48ab9f65 · outbound

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Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Unresolved cited work

Reference 30

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Observation 3f54172f-9912-4b15-bee3-751149969989 · outbound

This paper cites Using the nyström method to speed up kernel machines.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Using the nyström method to speed up kernel machines

Reference 31

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Observation ffdb59b9-5d17-4fd2-b7a7-0087ffa683ce · outbound

This paper cites Variational learning of inducing variables in sparse gaussian processes.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Variational learning of inducing variables in sparse gaussian processes

Reference 32

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Observation 26b943e7-cd98-4478-9fa1-309cbaf9f738 · outbound

This paper cites Scalable Variational Gaussian Process Classification.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Scalable Variational Gaussian Process Classification

Reference 33

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Observation 04dfdf2d-8ff8-4d36-b7e2-84233280d2d1 · outbound

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Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Unresolved cited work

Reference 34

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Observation f2db5b75-45b0-42ff-87e7-3963b550c2bc · outbound

This paper cites Maddox, Timur Garipov, Pavel Izmailov, Dmitry Vetrov, and Andrew Gordon Wilson.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Maddox, Timur Garipov, Pavel Izmailov, Dmitry Vetrov, and Andrew Gordon Wilson

Reference 35

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Observation abf21765-20de-44ea-a81a-542419a09714 · outbound

This paper cites Probabilistic predictions with fourier neural operators.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Probabilistic predictions with fourier neural operators

Reference 36

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Observation 65f46197-1c38-4880-8cdc-96b4b2089c31 · outbound

This paper cites Probabilistic neural operators for functional uncertainty quantification.Transactions on Machine Learning Research, 2025.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Probabilistic neural operators for functional uncertainty quantification.Transactions on Machine Learning Research, 2025

Reference 37

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Observation f829058d-0ac4-467e-9883-c382fcfbcd0d · outbound

This paper cites A simple approach to improve single-model deep uncertainty via distance-awareness.Journal of Machine Learning Research, 24(42):1–63, 2023.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning A simple approach to improve single-model deep uncertainty via distance-awareness.Journal of Machine Learning Research, 24(42):1–63, 2023

Reference 38

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Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Unresolved cited work

Reference 39

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Observation 4658404e-2043-4dd2-bd76-e3c166593757 · outbound

This paper cites A scalable laplace approximation for neural networks.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning A scalable laplace approximation for neural networks

Reference 40

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Observation dbf4c305-1caf-4d02-aa6f-cf9db44c75a7 · outbound

This paper cites Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-07-03T20:08:55.681504Z

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Observation 0b2cd81f-0c60-4e79-9688-c7356abd57b8 · outbound

This paper cites Uncertainty quantification for fourier neural operators.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Uncertainty quantification for fourier neural operators

Reference 42

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Observation 290dfa33-37e9-4f67-aad9-74062ae0daad · outbound

This paper cites Vecchia gaussian process ensembles on internal represen- tations of deep neural networks.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Vecchia gaussian process ensembles on internal represen- tations of deep neural networks

Reference 43

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Observation 393a2b9b-5145-47ec-bd4d-eaca832b98eb · outbound

This paper cites Kennedy and Anthony O’Hagan.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Kennedy and Anthony O’Hagan

Reference 44

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Observation 3f76bfb6-01e9-40ae-88aa-1f594d2eef41 · outbound

This paper cites Cavendish, John A.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Cavendish, John A

Reference 45

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Observation cede7d15-d804-4ff1-9ee2-89d70aec28b4 · outbound

This paper cites Computer model calibration or tuning in practice.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Computer model calibration or tuning in practice

Reference 46

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Observation dd0a7ec0-0b9c-4c55-b451-0936be016777 · outbound

This paper cites On the spectral bias of neural networks.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning On the spectral bias of neural networks

Reference 47

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Observation 24a2ba93-d662-44bb-bb9c-e3201f508dac · outbound

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Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Unresolved cited work

Reference 48

Resolution: parse uncertain; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation 9d7dc7c8-510f-4349-9945-e7a43871663d · outbound

This paper cites Layer by layer: Uncovering hidden representations in language models.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Layer by layer: Uncovering hidden representations in language models

Reference 49

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Observation 58e8a3c7-ba5d-44ca-966e-c9eb215afaf0 · outbound

This paper cites Visualizing data using t-sne.Journal of Machine Learning Research, 9(86):2579–2605, 2008.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Visualizing data using t-sne.Journal of Machine Learning Research, 9(86):2579–2605, 2008

Reference 50

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Observation ea0517f3-7143-4a03-8cf1-e2622859e322 · outbound

This paper cites Bayesian calibration of imperfect computer models using physics-informed priors.Journal of Machine Learning Research, 24(108):1–39, 2023.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Bayesian calibration of imperfect computer models using physics-informed priors.Journal of Machine Learning Research, 24(108):1–39, 2023

Reference 51

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Observation 6e7fc0f3-ef7b-41bb-9c0f-7919c12d8c32 · outbound

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Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Unresolved cited work

Reference 52

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Observation b8b32f8b-7909-47b4-a758-74c4c0f5df66 · outbound

This paper cites Similarity of Neural Network Representations Revisited.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Similarity of Neural Network Representations Revisited

Reference 53

Resolution: verified exact; local_arxiv, observed 2026-07-03T20:08:55.686402Z

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Observation 05b232b6-b249-4d23-9945-a385ce492d59 · outbound

This paper cites MacDonald, P.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning MacDonald, P

Reference 54

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Observation 4c2fcfcf-838f-4861-a6b5-bf9ab8e9f4a2 · outbound

This paper cites Gp+: A python library for kernel-based learning via gaussian processes.Advances in Engineering Software, 195:103686, 2024.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Gp+: A python library for kernel-based learning via gaussian processes.Advances in Engineering Software, 195:103686, 2024

Reference 55

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Observation 287155b4-1c29-4907-8d2b-534896eecffe · outbound

This paper cites an unresolved cited work.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Unresolved cited work

Reference 56

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Observation c03f5e83-cc9c-40dd-b03e-203e3cf38bd5 · outbound

This paper cites A mini-batch method for solving nonlinear pdes with gaussian processes, 2024.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning A mini-batch method for solving nonlinear pdes with gaussian processes, 2024

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Observation 4844ba6d-154e-44a6-bbfd-8752712ef7a9 · outbound

This paper cites Gomez, Łukasz Kaiser, and Illia Polosukhin.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Gomez, Łukasz Kaiser, and Illia Polosukhin

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Observation 8ac79d3c-8a4c-4aae-843a-24dfbbf3d5b6 · outbound

This paper cites Deep residual learning for image recognition, 2015.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Deep residual learning for image recognition, 2015

Reference 59

Resolution: unresolved; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation 05c5ab5b-2a29-4b4f-8e6a-4adedfcd6103 · outbound

This paper cites Gaussian error linear units (gelus), 2023.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Gaussian error linear units (gelus), 2023

Reference 60

Resolution: unresolved; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation 72275fd2-b64e-4087-83a0-3db33e10dd0d · outbound

This paper cites Decoupled weight decay regularization, 2019.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Decoupled weight decay regularization, 2019

Reference 61

Resolution: unresolved; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation 267a347e-9d8b-4582-8c28-68ae56244217 · outbound

This paper cites Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu

Reference 62

Resolution: unresolved; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation 5eedb604-1cde-4cd1-a758-34e6e9c06f23 · outbound

This paper cites Learning three-dimensional flow for interactive aerody- namic design.ACM Trans.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Learning three-dimensional flow for interactive aerody- namic design.ACM Trans

Reference 63

Resolution: unresolved; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation ba36db3b-2ade-4d51-a6c8-bc19db5f7d9a · outbound

This paper cites Test-time data augmentation for estimation of heteroscedastic aleatoric uncertainty in deep neural networks.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Test-time data augmentation for estimation of heteroscedastic aleatoric uncertainty in deep neural networks

Reference 64

Resolution: unresolved; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation 634d9cca-c4f6-41d8-8190-18a3c37bbd43 · outbound

This paper cites Specifically, instead of learning the map G† directly (which outputs an infinite-dimensional function), we learn the evaluation functional associated with the operator.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning Specifically, instead of learning the map G† directly (which outputs an infinite-dimensional function), we learn the evaluation functional associated with the operator

Reference 65

Resolution: malformed identifier; no resolver link, observed 2026-06-27T01:42:23.454308Z

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Observation 9a506e50-bf9b-4ae3-bfd3-7bc7a40ca3dd · outbound

This paper cites The architecture is configured based on the original setup to achieve near state-of-the-art predictive accuracy.

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning The architecture is configured based on the original setup to achieve near state-of-the-art predictive accuracy

Reference 66

Resolution: malformed identifier; no resolver link, observed 2026-06-27T01:42:23.454308Z

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