Paper Citation Record · LEDGER

An explainable operator approximation framework under the guideline of Green's function

As of 21 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2412.16644.

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pith.paper-citation-record.v1
2412.16644 v2

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measured 39 of 39 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-11T10:28:42.502623Z

measured 39 of 39 standing notices

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Reference resolution

39 of 39 outbound references displayed

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Outbound references

Observation 75279cc1-3598-486e-bb3c-8cf6994e1809 · outbound

This paper cites A general finite di fference method for arbitrary meshes.

An explainable operator approximation framework under the guideline of Green's function A general finite di fference method for arbitrary meshes

Reference 1

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Observation c8b3a8b8-9c96-47f5-8017-2ac2fc7af3c2 · outbound

This paper cites Finite element methods.

An explainable operator approximation framework under the guideline of Green's function Finite element methods

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:43.107195Z

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Observation f31b1965-6302-4609-9273-c6a2022179af · outbound

This paper cites Finite volume methods.

An explainable operator approximation framework under the guideline of Green's function Finite volume methods

Reference 3

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Observation 8c72b1d4-4b24-40b6-bca9-57f3611d6906 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

An explainable operator approximation framework under the guideline of Green's function Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 4

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Observation a9e50581-371d-4804-ae5a-89474cd849e5 · outbound

This paper cites Fourier neural operator for parametric partial differential equations.

An explainable operator approximation framework under the guideline of Green's function Fourier neural operator for parametric partial differential equations

Reference 5

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Observation abd0f2d5-40b2-4320-97c4-59b01431f9be · outbound

This paper cites Approximation theory of the mlp model in neural networks.

An explainable operator approximation framework under the guideline of Green's function Approximation theory of the mlp model in neural networks

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:43.059784Z

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Observation 08b84906-3404-4896-9ac9-64669a853a7a · outbound

This paper cites Physics-informed neural networks (PINNs) for fluid mechanics: A review.

An explainable operator approximation framework under the guideline of Green's function Physics-informed neural networks (PINNs) for fluid mechanics: A review

Reference 7

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Observation a47951a6-809d-4727-95d6-25672d510366 · outbound

This paper cites Learning the solution operator of parametric partial di fferential equations with physics- informed DeepONets.

An explainable operator approximation framework under the guideline of Green's function Learning the solution operator of parametric partial di fferential equations with physics- informed DeepONets

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T10:28:42.318381Z

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Observation 764bc8db-b62e-44e7-8b2b-fa2b57e44872 · outbound

This paper cites Multi-level neural networks for accurate solutions of boundary-value problems.

An explainable operator approximation framework under the guideline of Green's function Multi-level neural networks for accurate solutions of boundary-value problems

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:43.020985Z

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Observation 9930cdec-0a53-457e-8078-d058704c29d3 · outbound

This paper cites Theory-guided hard constraint projection (HCP): A knowledge-based data-driven scientific machine learning method.Journal of Computational Physics, 445:110624, 2021.

An explainable operator approximation framework under the guideline of Green's function Theory-guided hard constraint projection (HCP): A knowledge-based data-driven scientific machine learning method.Journal of Computational Physics, 445:110624, 2021

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:43.003487Z

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Observation b51be3de-ae51-415e-bc13-182b114fa453 · outbound

This paper cites Filtered partial di fferential equations: a robust surrogate constraint in physics-informed deep learning framework.

An explainable operator approximation framework under the guideline of Green's function Filtered partial di fferential equations: a robust surrogate constraint in physics-informed deep learning framework

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.985646Z

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Observation 8a5c20da-5093-4f73-abc9-bf5b70825e1a · outbound

This paper cites Ensemble of physics-informed neural networks for solving plane elasticity problems with examples.

An explainable operator approximation framework under the guideline of Green's function Ensemble of physics-informed neural networks for solving plane elasticity problems with examples

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.969296Z

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Observation 9a284e18-5d91-4720-8305-452a5eb59aa8 · outbound

This paper cites Probabilistic physics-informed neural network for seismic petrophysical inversion.

An explainable operator approximation framework under the guideline of Green's function Probabilistic physics-informed neural network for seismic petrophysical inversion

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.951472Z

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Observation 0731aa05-2f11-46be-8986-d73123d37519 · outbound

This paper cites Enhanced functional evaluation for the finite element penalty method.

An explainable operator approximation framework under the guideline of Green's function Enhanced functional evaluation for the finite element penalty method

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.934341Z

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Observation fcfb9d4f-42f3-4a74-acc1-ce85b7892de4 · outbound

This paper cites Weak adversarial networks for high-dimensional partial di fferential equations.

An explainable operator approximation framework under the guideline of Green's function Weak adversarial networks for high-dimensional partial di fferential equations

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.917982Z

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Observation 5f39951c-0e60-489d-b416-9220508a0ed0 · outbound

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

An explainable operator approximation framework under the guideline of Green's function Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 16

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Observation 630b6ad3-a09a-48fc-aad9-ce7b5888f987 · outbound

This paper cites The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems.

An explainable operator approximation framework under the guideline of Green's function The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T10:28:42.390945Z

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Observation 2dd2ed85-f3c2-472f-aecf-8b4991bcfff0 · outbound

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

An explainable operator approximation framework under the guideline of Green's function Fourier Neural Operator for Parametric Partial Differential Equations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T10:28:42.396341Z

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Observation 736975a6-df52-4501-852a-b9c25fb359aa · outbound

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

An explainable operator approximation framework under the guideline of Green's function Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T10:28:42.403532Z

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Observation 9d798202-45ac-41f4-a6a3-3a2cd5ec55de · outbound

This paper cites DeepOHeat: Operator learning-based ultra-fast thermal simulation in 3D-IC design.

An explainable operator approximation framework under the guideline of Green's function DeepOHeat: Operator learning-based ultra-fast thermal simulation in 3D-IC design

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.879512Z

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Observation da339681-654f-4e96-a586-6e293aa5eaf0 · outbound

This paper cites A fast general thermal simulation model based on Multi-Branch Physics-Informed deep operator neural network.

An explainable operator approximation framework under the guideline of Green's function A fast general thermal simulation model based on Multi-Branch Physics-Informed deep operator neural network

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.861693Z

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Observation 88500e60-010e-4958-9250-b4fe068e7923 · outbound

This paper cites DeepGreen: Deep learning of Green’s functions for nonlinear boundary value problems.

An explainable operator approximation framework under the guideline of Green's function DeepGreen: Deep learning of Green’s functions for nonlinear boundary value problems

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.843990Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b14abafa-9f56-461f-8985-1e1ba2268386 · outbound

This paper cites Data-driven discovery of Green’s functions with human-understandable deep learning.

An explainable operator approximation framework under the guideline of Green's function Data-driven discovery of Green’s functions with human-understandable deep learning

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.826564Z

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Observation b9d1d543-366d-4d3b-ad2f-9a841ec7bb74 · outbound

This paper cites Learning Green’s functions of linear reaction-diffusion equations with application to fast numerical solver.

An explainable operator approximation framework under the guideline of Green's function Learning Green’s functions of linear reaction-diffusion equations with application to fast numerical solver

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.810471Z

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Observation bcb064fc-ab16-498b-8eb7-0868bd853528 · outbound

This paper cites Operator approximation of the wave equation based on deep learning of Green’s function.

An explainable operator approximation framework under the guideline of Green's function Operator approximation of the wave equation based on deep learning of Green’s function

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.793216Z

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Observation 47b4d38a-2c9c-4a49-a663-4a5de74bcdd0 · outbound

This paper cites Learning domain-independent Green’s function for elliptic partial differential equations.

An explainable operator approximation framework under the guideline of Green's function Learning domain-independent Green’s function for elliptic partial differential equations

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.776922Z

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Observation 8835cd23-0eb0-41c6-9111-3fd334ad22c8 · outbound

This paper cites Rational neural networks.

An explainable operator approximation framework under the guideline of Green's function Rational neural networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.760956Z

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Observation f9f6610c-96d7-4f34-b44d-511e4bbbaff6 · outbound

This paper cites Gaussian processes for machine learning.

An explainable operator approximation framework under the guideline of Green's function Gaussian processes for machine learning

Reference 28

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Observation 065eb836-d41b-4b8c-85e0-a19378571445 · outbound

This paper cites Binary structured physics-informed neural networks for solving equations with rapidly changing solutions.

An explainable operator approximation framework under the guideline of Green's function Binary structured physics-informed neural networks for solving equations with rapidly changing solutions

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T10:28:42.452782Z

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Observation b9ff015e-8969-4aed-b06e-a442fca2a6a3 · outbound

This paper cites PaddlePaddle: An open-source deep learning platform from industrial practice.

An explainable operator approximation framework under the guideline of Green's function PaddlePaddle: An open-source deep learning platform from industrial practice

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.735093Z

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Observation 954ed2b0-472d-40f6-b12c-d3c8b4b3dae5 · outbound

This paper cites Learning elliptic partial di fferential equations with randomized linear algebra.

An explainable operator approximation framework under the guideline of Green's function Learning elliptic partial di fferential equations with randomized linear algebra

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.718271Z

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Observation c8edd16a-7dee-4338-ac48-cc45e726fe1c · outbound

This paper cites Adaptive mixtures of local experts.

An explainable operator approximation framework under the guideline of Green's function Adaptive mixtures of local experts

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.700795Z

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Observation bef82c8a-c364-4ff4-96b0-908d8de7b229 · outbound

This paper cites Monte Carlo strategies in scientific computing, volume 10.

An explainable operator approximation framework under the guideline of Green's function Monte Carlo strategies in scientific computing, volume 10

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-11T10:28:42.472257Z

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Observation 56fb358d-552f-4e4a-bbfe-994f85db0f28 · outbound

This paper cites Numerical methods for special functions.

An explainable operator approximation framework under the guideline of Green's function Numerical methods for special functions

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.672606Z

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Observation c6f5545f-7d38-49e0-b5be-5e084fc43aad · outbound

This paper cites Pfnn: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries.

An explainable operator approximation framework under the guideline of Green's function Pfnn: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.657586Z

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Observation 92a90edb-89b0-4c57-a078-236e374927e3 · outbound

This paper cites BINet: Learning to Solve Partial Differential Equations with Boundary Integral Networks.

An explainable operator approximation framework under the guideline of Green's function BINet: Learning to Solve Partial Differential Equations with Boundary Integral Networks

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-11T10:28:42.487327Z

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Observation 1abb43a1-ee98-48a7-8437-c6cf8622a781 · outbound

This paper cites Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks.

An explainable operator approximation framework under the guideline of Green's function Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.639819Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 990c5da6-f9bb-464f-9789-b44e57b4322a · outbound

This paper cites Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics.

An explainable operator approximation framework under the guideline of Green's function Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.622805Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d8b0bd1f-2b51-4cd7-9d9f-60ef1b4ee89e · outbound

This paper cites A note on the image system for a stokeslet in a no-slip boundary.

An explainable operator approximation framework under the guideline of Green's function A note on the image system for a stokeslet in a no-slip boundary

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:28:42.605948Z

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