Paper Citation Record · LEDGER

Physics-Informed Neural Operator for Learning Partial Differential Equations

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 41 inbound Pith citation observations for arXiv:2111.03794.

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pith.paper-citation-record.v1
2111.03794 v4

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measured 41 of 41 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:27:42.604629Z

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Source: pith, observed 2026-07-10T20:37:34.144100Z

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Pith citing papers

Observation 1d80ce4e-d7f2-45d3-a61a-185a259c830a · inbound

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems cites this paper.

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-24T12:44:28.940334Z

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Observation cce0c408-f920-4b0f-a10a-86c9f1a74bd3 · inbound

Generative diffusion learning for parametric partial differential equations cites this paper.

Generative diffusion learning for parametric partial differential equations Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-24T09:09:15.690960Z

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A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results cites this paper.

A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 56

Resolution: verified exact; arxiv_id, observed 2026-05-23T22:48:32.836450Z

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Observation 8972c031-f604-46c9-a280-10477a6fd08a · inbound

Graph-Based Operator Learning from Limited Data on Irregular Domains cites this paper.

Graph-Based Operator Learning from Limited Data on Irregular Domains Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 4

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Observation 9a527c3e-342a-467d-9194-f9cc4fce56df · inbound

PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations cites this paper.

PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-07T12:35:38.087349Z

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Observation d8a0a537-ca14-4dce-aa33-349711134b2e · inbound

Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory cites this paper.

Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-07T06:01:41.936709Z

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Observation bfe73ebd-9a82-4947-8514-173f2030406b · inbound

Operator-based machine learning framework for generalizable prediction of unsteady treatment dynamics in stormwater infrastructure cites this paper.

Operator-based machine learning framework for generalizable prediction of unsteady treatment dynamics in stormwater infrastructure Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 34

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Observation 275ecb16-bc20-45fe-8a49-1d485e4883ac · inbound

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction cites this paper.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.648801Z

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Observation ef7446d0-ddcf-4da5-95c6-c375b07f8f1b · inbound

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning cites this paper.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 8

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Observation 37e39ebc-606e-4ff6-9c62-e202c91f56f1 · inbound

FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning cites this paper.

FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-18T16:06:35.240921Z

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Observation 263ee996-8c98-48bf-a60e-4dba9c116a64 · inbound

Operator learning for models of tear film breakup cites this paper.

Operator learning for models of tear film breakup Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 47

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Observation 18ae9ca8-f8b4-4da6-a378-f12878761596 · inbound

Forward and Inverse Mantle Convection with Neural Operators cites this paper.

Forward and Inverse Mantle Convection with Neural Operators Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 2021

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Observation c4cbfb32-4a6a-4907-9138-1b73cf87b444 · inbound

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

Learning Neural Operator Surrogates for the Black Hole Accretion Code Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:21:23.713071Z

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Observation 9ca1fd42-75ca-4b4d-b530-b03f0fb4c857 · inbound

QuadNorm: Resolution-Robust Normalization for Neural Operators cites this paper.

QuadNorm: Resolution-Robust Normalization for Neural Operators Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 26

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T04:05:55.950346Z

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Observation fab23106-ab4b-49ce-a38f-d845b46f6b3b · inbound

Exactness Matters for Physical Rule Enforcement cites this paper.

Exactness Matters for Physical Rule Enforcement Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 24

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T03:26:19.840747Z

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Observation 272660d7-7543-4cb2-9e69-9551d0507037 · inbound

MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving cites this paper.

MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:41:30.494855Z

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Observation 39ec85a8-0832-4125-aa41-b346b637a844 · inbound

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations cites this paper.

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:16:30.442460Z

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Observation 4d7e6739-5bc6-4eb7-858a-67ce9e7dfdbc · inbound

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations cites this paper.

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 40

Resolution: verified exact; arxiv_id, observed 2026-05-13T07:12:28.204738Z

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Observation 4a02e600-b09d-4fc1-b056-95d2aec59390 · inbound

Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation cites this paper.

Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 34

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Observation d26eabb4-4982-4aff-bf78-c91cd7e6f43f · inbound

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs cites this paper.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.161744Z

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Observation d956efad-4a23-4762-88ec-6450de280022 · inbound

Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems cites this paper.

Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 22

Resolution: metadata mismatch; arxiv_id, observed 2026-05-19T19:23:13.037471Z

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Observation 93ba4be2-cc24-450a-9848-b42855489646 · inbound

Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment cites this paper.

Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 9

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Observation 1afabf19-0a9c-4eb5-9013-b469047edd91 · inbound

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models cites this paper.

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-22T07:14:42.355823Z

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Observation 17006866-65fb-45cd-a788-5732d43d40f1 · inbound

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models cites this paper.

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 31

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Observation a85c8ecd-530b-4666-afaf-8b359c512ecc · inbound

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models cites this paper.

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 31

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Observation b46ee441-4f8b-407c-a0a7-bf24929e9a10 · inbound

Semigroup Consistency as a Diagnostic for Learned Physics Simulators cites this paper.

Semigroup Consistency as a Diagnostic for Learned Physics Simulators Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-06-29T22:24:00.368947Z

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Observation bffe3330-c994-4969-b9cf-85ecf5c415f8 · inbound

Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations cites this paper.

Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 27

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Observation 2fe98728-2c26-4172-a60a-d97d98a37d05 · inbound

Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System cites this paper.

Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-06-29T14:43:30.802357Z

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Observation 5482668d-8cc0-47d0-91b6-d7c01f507513 · inbound

Data-driven surrogate models for forecasting experimentally measured fluid flows cites this paper.

Data-driven surrogate models for forecasting experimentally measured fluid flows Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 46

Resolution: verified exact; arxiv_id, observed 2026-07-03T07:47:44.535601Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ede221a8-ceb9-4127-805b-8fec4169215b · inbound

Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers cites this paper.

Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:59:40.341886Z

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Observation 2d21c960-d8c2-4f76-8041-643836cb81ab · inbound

Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow cites this paper.

Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-07-04T18:50:04.824056Z

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Observation eff51154-1809-4560-9ced-cdb04afefb13 · inbound

Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow cites this paper.

Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 24

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Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics cites this paper.

Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 12

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CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts cites this paper.

CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-07-10T20:37:34.145595Z

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Observation 7ed91fe8-2264-44a1-bd0e-ae14114b7906 · inbound

CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts cites this paper.

CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 22

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Observation 6137b445-37b0-4c95-a688-89b514b22e0a · inbound

DRIFT: Direct Reduced Fourier Transforms for Distributed Spectral Neural Operators cites this paper.

DRIFT: Direct Reduced Fourier Transforms for Distributed Spectral Neural Operators Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 6

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Observation 1cf982a6-ac44-46ca-af75-d682f309bd34 · inbound

Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows cites this paper.

Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 31

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Observation 51a9daa6-e7d3-4a05-adde-191e5ecda24f · inbound

Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation cites this paper.

Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 16

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Observation 5f70d266-d819-4d74-a442-320219600846 · inbound

A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates cites this paper.

A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 19

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Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators cites this paper.

Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 6

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Observation 83766a30-97a7-4d92-b207-a9a23bc2bd49 · inbound

Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation cites this paper.

Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 35

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Unavailable: canonical work link unavailable.