A comprehensive analysis of PINNs: Variants, Applications, and Challenges | Paper Citation Record

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This paper cites Dynamic programming.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Dynamic programming

Reference 1

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This paper cites Three ways to solve partial differential equations with neural networks—a review.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Three ways to solve partial differential equations with neural networks—a review

Reference 2

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

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Artificial neural networks for solving ordinary and partial differential equations

Reference 3

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

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 4

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This paper cites Scientific machine learning through physics–informed neural networks: Where we are and what’s next.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Scientific machine learning through physics–informed neural networks: Where we are and what’s next

Reference 5

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This paper cites Physics-informed neural network (pinn) evolution and beyond: A systematic literature review and bibliometric analysis.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural network (pinn) evolution and beyond: A systematic literature review and bibliometric analysis

Reference 6

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This paper cites A review of physics-informed machine learning in fluid mechanics.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges A review of physics-informed machine learning in fluid mechanics

Reference 7

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This paper cites Applications of physics-informed neural networks in power systems - a review.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Applications of physics-informed neural networks in power systems - a review

Reference 8

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges Unresolved cited work

Reference 9

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This paper cites Training generative adversarial networks by solving ordinary differential equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Training generative adversarial networks by solving ordinary differential equations

Reference 10

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This paper cites Meade and A.A.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Meade and A.A

Reference 12

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This paper cites Regression-based neural network training for the solution of ordinary differential equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Regression-based neural network training for the solution of ordinary differential equations

Reference 13

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This paper cites Application neural network to solve ordinary differential equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Application neural network to solve ordinary differential equations

Reference 14

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This paper cites Solving ordinary differential equations using wavelet neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Solving ordinary differential equations using wavelet neural networks

Reference 15

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This paper cites Nascimento, Kajetan Fricke, and Felipe A.C.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Nascimento, Kajetan Fricke, and Felipe A.C

Reference 16

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This paper cites Solving ordinary differential equations using an optimization technique based on training improved artificial neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Solving ordinary differential equations using an optimization technique based on training improved artificial neural networks

Reference 17

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This paper cites Viana, Renato G.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Viana, Renato G

Reference 18

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This paper cites Hyperpinn: Learning parameterized differential equations with physics-informed hypernetworks, 2021.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Hyperpinn: Learning parameterized differential equations with physics-informed hypernetworks, 2021

Reference 19

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This paper cites Physics-informed neural network: The effect of reparameterization in solving differential equations, 2023.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural network: The effect of reparameterization in solving differential equations, 2023

Reference 20

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This paper cites Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark tests, 2023.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark tests, 2023

Reference 21

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This paper cites Solving stiff ordinary differential equations using physics informed neural networks (pinns): simple recipes to improve training of vanilla-pinns, 2023.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Solving stiff ordinary differential equations using physics informed neural networks (pinns): simple recipes to improve training of vanilla-pinns, 2023

Reference 22

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

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Learning in modal space: Solving time-dependent stochastic pdes using physics-informed neural networks

Reference 23

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges Unresolved cited work

Reference 24

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Observation 7aa11c0c-d322-445d-ba73-e56a3a00e959 · outbound

This paper cites Physics-informed neural networks for solving coupled stokes-darcy equation.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural networks for solving coupled stokes-darcy equation

Reference 25

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This paper cites Spectrally adapted physics-informed neural networks for solv- ing unbounded domain problems.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Spectrally adapted physics-informed neural networks for solv- ing unbounded domain problems

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This paper cites A second-order network structure based on gradient-enhanced physics-informed neural networks for solving parabolic partial differential equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges A second-order network structure based on gradient-enhanced physics-informed neural networks for solving parabolic partial differential equations

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This paper cites Wight and Jia Zhao.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Wight and Jia Zhao

Reference 28

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This paper cites Mukhametzhanov.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Mukhametzhanov

Reference 29

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This paper cites Singh, Dharminder Chaudhary, B.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Singh, Dharminder Chaudhary, B

Reference 30

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This paper cites A physics-informed neural network framework for pdes on 3d surfaces: Time independent problems.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges A physics-informed neural network framework for pdes on 3d surfaces: Time independent problems

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This paper cites Physics informed rnn-dct networks for time-dependent partial differential equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics informed rnn-dct networks for time-dependent partial differential equations

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Observation 9947d1c8-008f-457b-9678-a3e0e897d97e · outbound

This paper cites A hybrid physics-informed neural network for nonlinear partial differential equation, 2021.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges A hybrid physics-informed neural network for nonlinear partial differential equation, 2021

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This paper cites Mistani, Miguel A.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Mistani, Miguel A

Reference 34

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This paper cites A universal pinns method for solving partial differential equations with a point source.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges A universal pinns method for solving partial differential equations with a point source

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This paper cites Mitigating coordinate transformation for solving partial differential equations with physic-informed neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Mitigating coordinate transformation for solving partial differential equations with physic-informed neural networks

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This paper cites Phycrnet: Physics-informed convolutional- recurrent network for solving spatiotemporal pdes.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Phycrnet: Physics-informed convolutional- recurrent network for solving spatiotemporal pdes

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This paper cites Adversarial multi-task learning enhanced physics- informed neural networks for solving partial differential equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Adversarial multi-task learning enhanced physics- informed neural networks for solving partial differential equations

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This paper cites Hierarchical learning to solve pdes using physics-informed neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Hierarchical learning to solve pdes using physics-informed neural networks

Reference 39

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges Popovych

Reference 40

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This paper cites Parametric compressible flow predictions using physics- informed neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Parametric compressible flow predictions using physics- informed neural networks

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This paper cites Physics-informed neural networks for parametric compressible euler equations, 2023.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural networks for parametric compressible euler equations, 2023

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Observation a7a95c91-f81d-4276-81b3-a9a81ebfcb3f · outbound

This paper cites fpinns: Fractional physics-informed neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges fpinns: Fractional physics-informed neural networks

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This paper cites Laplace-fpinns: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion, 2023.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Laplace-fpinns: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion, 2023

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Observation 66f9b4af-c37b-429b-9f79-730a59674730 · outbound

This paper cites Fractional physics-informed neural networks for time-fractional phase field models.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Fractional physics-informed neural networks for time-fractional phase field models

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges Unresolved cited work

Reference 46

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This paper cites Physics-informed neural network algorithm for solv- ing forward and inverse problems of variable-order space-fractional advection–diffusion equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural network algorithm for solv- ing forward and inverse problems of variable-order space-fractional advection–diffusion equations

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Observation 80c3e3fb-aee2-40f8-bfac-bffa027c722c · outbound

This paper cites Fractional chebyshev deep neural network (fcdnn) for solving differential models.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Fractional chebyshev deep neural network (fcdnn) for solving differential models

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Observation 6f6c0d30-5326-4b5b-8c81-b2440bb62456 · outbound

This paper cites Bi-orthogonal fpinn: A physics- informed neural network method for solving time-dependent stochastic fractional pdes, 2023.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Bi-orthogonal fpinn: A physics- informed neural network method for solving time-dependent stochastic fractional pdes, 2023

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This paper cites A class of improved fractional physics informed neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges A class of improved fractional physics informed neural networks

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This paper cites Jagtap, Ehsan Kharazmi, and George Em Karniadakis.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Jagtap, Ehsan Kharazmi, and George Em Karniadakis

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Observation 0b6cd2da-1e86-44e4-95ee-7597bdcbb96e · outbound

This paper cites Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations

Reference 52

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Observation a9a572da-28e1-4855-9b51-6f97682d9cc3 · outbound

This paper cites Jagtap, George Em Karniadakis, and Kenji Kawaguchi.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Jagtap, George Em Karniadakis, and Kenji Kawaguchi

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Observation 75185bf8-e499-43e9-8eb4-7788674b625c · outbound

This paper cites A dimension-augmented physics- informed neural network (dapinn) with high level accuracy and efficiency.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges A dimension-augmented physics- informed neural network (dapinn) with high level accuracy and efficiency

Reference 54

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Observation 9af79d4a-0e4c-489a-9f36-abaf7d651840 · outbound

This paper cites Distributed physics informed neural network for data-efficient solution to partial differential equations, 2019.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Distributed physics informed neural network for data-efficient solution to partial differential equations, 2019

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:08.389901Z

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Observation 10cc580c-22ad-4678-81aa-5f8e1b6a963c · outbound

This paper cites Fuhg, Ioannis Kalogeris, Amélie Fau, and Nikolaos Bouklas.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Fuhg, Ioannis Kalogeris, Amélie Fau, and Nikolaos Bouklas

Reference 56

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Observation f889eb41-a686-43ff-a5d0-4482697a4bed · outbound

This paper cites Pignet: a physics-informed deep learning model toward generalized drug–target interaction predictions.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Pignet: a physics-informed deep learning model toward generalized drug–target interaction predictions

Reference 57

Resolution: verified exact; doi, observed 2026-08-07T13:05:00.650188Z

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Observation 5159cbc7-1d87-49d2-9689-96af0c6292c1 · outbound

This paper cites Physics-informed neural networks for brain hemo- dynamic predictions using medical imaging.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural networks for brain hemo- dynamic predictions using medical imaging

Reference 58

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Observation 056b55aa-16e0-44c0-a571-d39089d1458b · outbound

This paper cites Physics-informed neural networks (pinns) for 4d hemodynamics prediction: An investigation of optimal framework based on vascular morphology.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed neural networks (pinns) for 4d hemodynamics prediction: An investigation of optimal framework based on vascular morphology

Reference 59

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Observation 5a8bce55-1514-471f-8a3d-728f91db99ed · outbound

This paper cites Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:08.310299Z

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Observation ed4567dc-314d-4c35-bf18-b9a7a98928b9 · outbound

This paper cites Hurtado, and Ellen Kuhl.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Hurtado, and Ellen Kuhl

Reference 61

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Observation b89485b2-8a66-4274-844a-db692d984c02 · outbound

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges Unresolved cited work

Reference 62

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Observation 5d65d1b5-5928-44b5-8487-39e77dfa555b · outbound

This paper cites Gradient-enhanced physics-informed neural networks for power systems operational support.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Gradient-enhanced physics-informed neural networks for power systems operational support

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:08.194867Z

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Observation 3b801aad-8f42-4ead-8278-200828e27783 · outbound

This paper cites Dae-pinn: a physics-informed neural network model for simulating differential algebraic equations with application to power networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Dae-pinn: a physics-informed neural network model for simulating differential algebraic equations with application to power networks

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:08.082705Z

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Observation 9c1286e1-ea75-462b-ab1c-a81f766a9141 · outbound

This paper cites Raissi, P.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Raissi, P

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-07T13:04:58.683380Z

Source-reported events for the cited work

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Observation 2564fc1f-29bf-454d-86fc-8ebfd11f6ee7 · outbound

This paper cites Physics-informed deep learning for data-driven solutions of computational fluid dynamics.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics-informed deep learning for data-driven solutions of computational fluid dynamics

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:07.937658Z

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Observation 46575a10-fc12-4d3f-a6a9-2740f194db4e · outbound

This paper cites Jagtap, Zhiping Mao, Nikolaus Adams, and George Em Karniadakis.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Jagtap, Zhiping Mao, Nikolaus Adams, and George Em Karniadakis

Reference 67

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Observation 2a687aa7-69bb-4d97-a6c5-e6f08b870156 · outbound

This paper cites Predicting high- fidelity multiphysics data from low-fidelity fluid flow and transport solvers using physics-informed neu- ral networks.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Predicting high- fidelity multiphysics data from low-fidelity fluid flow and transport solvers using physics-informed neu- ral networks

Reference 68

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T13:05:02.637718Z

Source-reported events for the cited work

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Observation 801743a9-9d4e-4a96-a45f-3834e940f8c6 · outbound

This paper cites Physics informed neural networks for surrogate modeling of accidental scenarios in nuclear power plants.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Physics informed neural networks for surrogate modeling of accidental scenarios in nuclear power plants

Reference 69

Resolution: verified exact; doi, observed 2026-08-07T13:05:00.123537Z

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Observation f0d27710-8479-404b-97ef-5ab6438d0a8c · outbound

This paper cites Badia, and Lluís Jofre.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Badia, and Lluís Jofre

Reference 70

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Observation af82df86-2a15-4589-86ba-9925fb0f40b0 · outbound

This paper cites Research progress of physics-informed neural network in seismic wave modeling.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Research progress of physics-informed neural network in seismic wave modeling

Reference 71

Resolution: verified exact; doi, observed 2026-08-07T13:04:59.942708Z

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Observation 9a5fffe5-1b6f-4bb6-9e00-ced586720f23 · outbound

This paper cites Using a physics- informed neural network and fault zone acoustic monitoring to predict lab earthquakes.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Using a physics- informed neural network and fault zone acoustic monitoring to predict lab earthquakes

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:07.767590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8ba3abd5-b1a1-433a-93cc-8bdbe58f5206 · outbound

This paper cites Modeling water flow and solute transport in unsaturated soils using physics-informed neural networks trained with geoelectrical data.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges Modeling water flow and solute transport in unsaturated soils using physics-informed neural networks trained with geoelectrical data

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:07.646557Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e0675457-d7d7-47f4-b139-b51627be035f · outbound

This paper cites URL https://www.sciencedirect.com/science/ article/pii/S0960077921008845.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges URL https://www.sciencedirect.com/science/ article/pii/S0960077921008845

Reference 779

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T13:05:05.256153Z

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Observation 0a2b5f32-52c0-4e6a-94ee-b28eea4fa2cb · outbound

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges URL https://www.sciencedirect.com/science/ article/pii/0895717794900957

Reference 7177

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Observation a25a51aa-6dd5-4d84-8ff4-2de0bfaf4d9d · outbound

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges URL https://www.sciencedirect.com/science/ article/pii/S0378779623004406

Reference 7796

Resolution: unresolved; no resolver link, observed 2026-08-07T13:04:58.502547Z

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Observation 26cfed13-9138-4d1b-b03b-3e0fcbdf530f · outbound

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A comprehensive analysis of PINNs: Variants, Applications, and Challenges URL https://www.sciencedirect.com/science/ article/pii/S0045782520302127

Reference 7825

Resolution: unresolved; no resolver link, observed 2026-08-07T13:04:57.095522Z

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Observation 1915fa7a-9141-44fc-a5e8-36425fcd4649 · outbound

This paper cites URL https://www.sciencedirect.com/science/ article/pii/S1361841521001122.

A comprehensive analysis of PINNs: Variants, Applications, and Challenges URL https://www.sciencedirect.com/science/ article/pii/S1361841521001122

Reference 8415

Resolution: unresolved; no resolver link, observed 2026-08-07T13:04:58.076209Z

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