Paper Citation Record · LEDGER

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective

As of 20 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2506.19805.

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

pith.paper-citation-record.v1
2506.19805 v2

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:29:43.767706Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T15:51:30.007369Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T15:51:30.175198Z

Reference resolution

46 of 46 outbound references displayed

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External citation measurements

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Outbound references

Observation e001a3c8-76d6-47c0-9da6-447d8cac9d31 · outbound

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

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 1

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Observation a0302b7b-3418-4a83-8ac6-bc6ea81f3d74 · outbound

This paper cites Physics- informed machine learning.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics- informed machine learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.596533Z

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Observation aae7dde3-0a30-4d7d-9d78-861865cbe872 · outbound

This paper cites Physics-informed neural networks for studying heat transfer in porous media.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-informed neural networks for studying heat transfer in porous media

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.601119Z

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Observation 89993a11-48ab-4002-98ca-37fa1359c459 · outbound

This paper cites Physics-informed neural networks for heat transfer problems.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-informed neural networks for heat transfer problems

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.605075Z

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Observation 18c5a589-b03a-4d30-8b2d-15df72a7ae9f · outbound

This paper cites Hxpinn: A hypernetwork-based physics-informed neural network for real-time monitoring of an industrial heat exchanger.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Hxpinn: A hypernetwork-based physics-informed neural network for real-time monitoring of an industrial heat exchanger

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.202576Z

Source-reported events for the cited work

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Observation a7d3ef00-7cce-4caa-95b9-9e32ae6222e2 · outbound

This paper cites Physics-informed neural networks (PINN) for computational solid mechanics: Numerical frameworks and applications.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-informed neural networks (PINN) for computational solid mechanics: Numerical frameworks and applications

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.191120Z

Source-reported events for the cited work

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Observation 208ab9ae-1eec-499f-a4d6-5b240bb8847b · outbound

This paper cites Physics-guided, physics-informed, and physics-encoded neural networks and operators in scientific computing: Fluid and solid mechanics.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-guided, physics-informed, and physics-encoded neural networks and operators in scientific computing: Fluid and solid mechanics

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.179365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ad784ae3-d01e-477e-b9b0-90b361955f0c · outbound

This paper cites Learning in modal space: Solving time-dependent stochastic PDEs using physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Learning in modal space: Solving time-dependent stochastic PDEs using physics-informed neural networks

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.165813Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5d2479b4-fbef-4740-9a8e-b61445cfe481 · outbound

This paper cites Solving inverse stochastic problems from discrete particle observations using the Fokker–Planck equation and physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Solving inverse stochastic problems from discrete particle observations using the Fokker–Planck equation and physics-informed neural networks

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.154352Z

Source-reported events for the cited work

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Observation d15ccddf-daf9-42dc-9316-88989360df87 · outbound

This paper cites Adversarial uncertainty quantification in physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Adversarial uncertainty quantification in physics-informed neural networks

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.631365Z

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Observation ced88231-d080-491c-b3f1-97c5ef6382e7 · outbound

This paper cites Quantifying total uncertainty in physics- informed neural networks for solving forward and inverse stochastic problems.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Quantifying total uncertainty in physics- informed neural networks for solving forward and inverse stochastic problems

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.137575Z

Source-reported events for the cited work

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Observation dc12b8b3-b068-404b-9695-10dc9b1164c0 · outbound

This paper cites B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.638516Z

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Observation aa449572-9077-4bba-b690-5ece584c9f38 · outbound

This paper cites Physics-constrained learning of PDE systems with uncertainty quantified port-hamiltonian models.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-constrained learning of PDE systems with uncertainty quantified port-hamiltonian models

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.119765Z

Source-reported events for the cited work

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Observation 7f601000-5db3-4804-9787-4722477f7b95 · outbound

This paper cites Plug-and-Play Physics-informed Learning using Uncertainty Quantified Port-Hamiltonian Models.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Plug-and-Play Physics-informed Learning using Uncertainty Quantified Port-Hamiltonian Models

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:29:43.877273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ad98363f-8bf2-48e1-800d-fdef3e60d30e · outbound

This paper cites PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.649584Z

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Observation 92e24a3b-3245-4880-b4b8-76526f0dbab8 · outbound

This paper cites DiffusionPDE: Generative PDE-Solving Under Partial Observation.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective DiffusionPDE: Generative PDE-Solving Under Partial Observation

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.653387Z

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Observation e02c6396-e865-4666-837d-76a06433835b · outbound

This paper cites Physics-Informed Diffusion Models.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-Informed Diffusion Models

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.656904Z

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Observation 5b844bd8-a5c6-4452-8858-bc18176b6812 · outbound

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

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.661120Z

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Observation 79d3e5a1-464c-472b-a5d3-58160f52317a · outbound

This paper cites Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.664698Z

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Observation eefcbb23-883e-4a64-b733-06790c4acdee · outbound

This paper cites Coordinate transform fourier neural operators for symmetries in physical modelings.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Coordinate transform fourier neural operators for symmetries in physical modelings

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.109124Z

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Observation 25c19103-20e0-48c5-be4e-793191ce8e8f · outbound

This paper cites Laplace neural operator for solving differential equations.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Laplace neural operator for solving differential equations

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.673339Z

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Observation ae756543-ad57-46c1-b9f7-18726520d972 · outbound

This paper cites Understanding and mitigating gradient flow pathologies in physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Understanding and mitigating gradient flow pathologies in physics-informed neural networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.677216Z

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Observation d9acb6bc-1772-44c3-8ec4-b57127494b4d · outbound

This paper cites Residual- based attention in physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Residual- based attention in physics-informed neural networks

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.680446Z

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Observation 01882c1b-684a-4052-a8df-c461c36786c7 · outbound

This paper cites Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.683788Z

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Observation f987a507-06a1-41a8-a7ad-546545265867 · outbound

This paper cites Discontinuity computing using physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Discontinuity computing using physics-informed neural networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.077729Z

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Observation 63780de2-8d7f-48a3-9cc3-3c28268a4338 · outbound

This paper cites Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.066366Z

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Observation 0a6a5b05-f749-4181-aadc-2a90fa4bf8ee · outbound

This paper cites On the application of physics informed neural networks (PINN) to solve boundary layer thermal-fluid problems.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective On the application of physics informed neural networks (PINN) to solve boundary layer thermal-fluid problems

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.055534Z

Source-reported events for the cited work

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Observation 24035272-8ebe-4e2f-9050-7d6346c9c9cc · outbound

This paper cites DeepXDE: A deep learning library for solving differential equations.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective DeepXDE: A deep learning library for solving differential equations

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.701746Z

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Observation 86055078-976f-4fbe-9f71-1999265979b6 · outbound

This paper cites A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.705464Z

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Observation 67131b71-d855-4bee-b7db-344f4e1e3680 · outbound

This paper cites Failure-informed adaptive sampling for PINNs.SIAM Journal on Scientific Computing, 45(4):A1971–A1994, 2023.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Failure-informed adaptive sampling for PINNs.SIAM Journal on Scientific Computing, 45(4):A1971–A1994, 2023

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.030596Z

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Observation c4acdfbe-fb49-49dc-8088-046b3226f0de · outbound

This paper cites Active learning based sampling for high-dimensional nonlinear partial differential equations.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Active learning based sampling for high-dimensional nonlinear partial differential equations

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.713039Z

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Unavailable: canonical work link unavailable.

Observation a4c72c24-3f9a-4fe9-9640-b2dd73e2d03f · outbound

This paper cites Multi-objective loss balancing for physics-informed deep learning.Computer Methods in Applied Mechanics and Engineering, 439:117914, 2025.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Multi-objective loss balancing for physics-informed deep learning.Computer Methods in Applied Mechanics and Engineering, 439:117914, 2025

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.716494Z

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Observation e7c4df57-20b3-435f-986d-2cbc1b1b4827 · outbound

This paper cites When and why PINNs fail to train: A neural tangent kernel perspective.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective When and why PINNs fail to train: A neural tangent kernel perspective

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:44.007601Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 53e0cbb8-317c-4597-8dff-0076c0ec4d6a · outbound

This paper cites Self-adaptive loss balanced physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Self-adaptive loss balanced physics-informed neural networks

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.726620Z

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Unavailable: canonical work link unavailable.

Observation a19773a2-957c-44b9-857d-3b6f81a4fdf6 · outbound

This paper cites Physics-informed neural networks with weighted losses by uncertainty evaluation for accurate and stable prediction of manufacturing systems.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-informed neural networks with weighted losses by uncertainty evaluation for accurate and stable prediction of manufacturing systems

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:43.988089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c9522714-49df-4adc-a342-10523a129ae9 · outbound

This paper cites Loss-attentional physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Loss-attentional physics-informed neural networks

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.733858Z

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Observation 6dc5a96a-b854-4e06-bd15-8a67718bfe99 · outbound

This paper cites An imbalanced learning-based sampling method for physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective An imbalanced learning-based sampling method for physics-informed neural networks

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:43.970278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 97971d33-f6e5-4ddf-a6af-d650025fb968 · outbound

This paper cites Physics- informed neural networks with hard constraints for inverse design.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics- informed neural networks with hard constraints for inverse design

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:43.959186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 45fc93f6-17af-43c1-900f-b6578ae0188d · outbound

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

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.743679Z

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Observation 9e680e4b-6693-4b87-8132-4f641e82f001 · outbound

This paper cites A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.747059Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a194e8f0-5394-41cc-a9e6-a2b69b2f1505 · outbound

This paper cites Self-adaptive physics-informed neural networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Self-adaptive physics-informed neural networks

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.750415Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75dc8ea7-72ea-495d-9662-9f4c901982ff · outbound

This paper cites RoPINN: Region Optimized Physics-Informed Neural Networks.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective RoPINN: Region Optimized Physics-Informed Neural Networks

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.753703Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 936d4f71-1d92-476e-a735-80b670aa8fbb · outbound

This paper cites https://github.com/Shengfeng233/PINN-for-NS-equation.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective https://github.com/Shengfeng233/PINN-for-NS-equation

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:43.927156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b8ddeeea-44c0-4921-8047-df184bb859c1 · outbound

This paper cites Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:43.912925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9c153719-930b-488b-a994-20d9392266c5 · outbound

This paper cites NSFnets (Navier-Stokes flow nets): Physics- informed neural networks for the incompressible Navier-Stokes equations.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective NSFnets (Navier-Stokes flow nets): Physics- informed neural networks for the incompressible Navier-Stokes equations

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-15T18:29:43.764324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8608c793-c6e6-4eb6-8fcd-31b3c6c99361 · outbound

This paper cites Pinnacle: A comprehensive benchmark of physics-informed neural networks for solving PDEs.

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective Pinnacle: A comprehensive benchmark of physics-informed neural networks for solving PDEs

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:29:43.893526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 229ee2d3-73d7-4d43-9a85-a1118b3c9b68 · inbound

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks cites this paper.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:51:30.178129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.