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Paper Citation Record · LEDGER

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks

As of 20 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2506.17726.

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

pith.paper-citation-record.v1
2506.17726 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:06:47.994755Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

49 of 49 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 56d85523-1e12-44b9-852e-071f1c82f69a · outbound

This paper cites TensorFlow: A system for large-scale machine learning.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks TensorFlow: A system for large-scale machine learning

Reference 1

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Observation 7baa8b57-2873-45fc-8fcc-39a9128c2124 · outbound

This paper cites Automatic Differentiation in Machine Learning: A Survey.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Automatic Differentiation in Machine Learning: A Survey

Reference 2

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Observation f45e7b55-9aad-4420-9860-7eb803debd3f · outbound

This paper cites Burgers' pinns with implicit euler transfer learning.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Burgers' pinns with implicit euler transfer learning

Reference 3

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Observation e0ee2abb-3232-44a3-9f99-0f32b5271596 · outbound

This paper cites Partition of Unity Methods.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Partition of Unity Methods

Reference 4

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Observation b3545a0b-f0a6-4737-a52e-ffa74a51d19f · outbound

This paper cites Jax: Autograd and xla.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Jax: Autograd and xla

Reference 5

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Observation 530d2171-7c44-409d-9489-4aa0f9d88a03 · outbound

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

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Physics-informed neural networks for heat transfer problems

Reference 6

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Observation 04202a64-9d97-4db9-8c43-4eabe9d2a11d · outbound

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

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Physics-informed neural networks (PINNs) for fluid mechanics: A review

Reference 7

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Observation 16f1ed54-3996-4b7a-af0b-c3e4b5ec3212 · outbound

This paper cites Distributed learning machines for solving forward and inverse problems in partial differential equations.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Distributed learning machines for solving forward and inverse problems in partial differential equations

Reference 8

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Observation 6e19c613-2387-4b16-aeed-11cb32ec1986 · outbound

This paper cites Physics Informed Extreme Learning Machine (PIELM) – A rapid method for the numerical solution of partial differential equations.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Physics Informed Extreme Learning Machine (PIELM) – A rapid method for the numerical solution of partial differential equations

Reference 9

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Observation d2333458-5845-4f74-96a3-8b2f5e3d983a · outbound

This paper cites Physics-informed kernel function neural networks for solving partial differential equations.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Physics-informed kernel function neural networks for solving partial differential equations

Reference 10

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Observation 1176ad3a-b9e9-49fb-bb01-a709718e0c3a · outbound

This paper cites Physical informed neural network for thermo-hydral analysis of fire-loaded concrete.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Physical informed neural network for thermo-hydral analysis of fire-loaded concrete

Reference 11

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Observation c888ea1f-7fc6-40c8-96a4-b4a204831c44 · outbound

This paper cites An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

Reference 12

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Observation 9cdaeb9b-897a-49a7-a8e9-2871bcb7662c · outbound

This paper cites Transfer learning enhanced physics informed neural network for phase-field modeling of fracture.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

Reference 13

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Observation ddb5027a-27ae-4ef5-b7db-e8e9886fd2db · outbound

This paper cites A deep learning framework for solution and discovery in solid mechanics.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks A deep learning framework for solution and discovery in solid mechanics

Reference 14

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Observation cb102a52-50b6-4300-9340-ca2587809739 · outbound

This paper cites Deep learning in computational mechanics: a review.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Deep learning in computational mechanics: a review

Reference 15

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Source-reported events for the cited work

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Observation b15859d9-de55-484c-a5f3-6d1ac485d8c7 · outbound

This paper cites Long Short-term Memory.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Long Short-term Memory

Reference 16

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Observation fbcdcbec-bb1c-46fe-8a17-7a78bf3278cf · outbound

This paper cites Multilayer feedforward networks are universal approximators.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Multilayer feedforward networks are universal approximators

Reference 17

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Observation 6f76bfaa-fa53-49cb-b884-762a7af0d0af · outbound

This paper cites Solving heat conduction problems with a moving heat source in arc welding processes via an overlapping nodes scheme based on the improved element- free Galerkin method.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Solving heat conduction problems with a moving heat source in arc welding processes via an overlapping nodes scheme based on the improved element- free Galerkin method

Reference 18

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Observation c256326f-8fa7-40bf-a0d1-aa1c0f94d7be · outbound

This paper cites hp-VPINNs: Variational physics-informed neural networks with domain decomposition.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks hp-VPINNs: Variational physics-informed neural networks with domain decomposition

Reference 19

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Observation 3b2547d5-7ef2-42d3-8559-777bd405fc7c · outbound

This paper cites Variational Physics-Informed Neural Networks For Solving Partial Differential Equations.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 20

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Observation 1c0ebb22-2015-4c85-8515-64c0300e370c · outbound

This paper cites Adaptive finite element solution for the heat conduction with a moving heat source.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Adaptive finite element solution for the heat conduction with a moving heat source

Reference 21

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Observation 881ef635-4458-402e-a6c4-ae7722360ff6 · outbound

This paper cites Temperature Field Due to a Moving Heat Source: A Moving Mesh Finite Element Analysis.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Temperature Field Due to a Moving Heat Source: A Moving Mesh Finite Element Analysis

Reference 22

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Observation 8b9d407b-22b6-4971-a0a5-823e724c866a · outbound

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

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Artificial neural networks for solving ordinary and partial differential equations

Reference 23

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Observation 2f3389bb-f24c-425d-b747-0f5741fd828f · outbound

This paper cites Neural-network methods for boundary value problems with irregular boundaries.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Neural-network methods for boundary value problems with irregular boundaries

Reference 24

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Observation 2b20f86a-ab21-43e8-92ab-b697a8147420 · outbound

This paper cites Reynolds averaged turbulence mod- elling using deep neural networks with embedded invariance.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Reynolds averaged turbulence mod- elling using deep neural networks with embedded invariance

Reference 25

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Observation 98f9670e-0be7-4faf-92b2-b4264b8ee87d · outbound

This paper cites A review of automatic differentiation and its efficient implementa- tion.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks A review of automatic differentiation and its efficient implementa- tion

Reference 26

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Observation 2f22987a-820e-4691-a502-cefb77fe2e17 · outbound

This paper cites An efficient boundary-type meshfree method for analysis of two-dimensional laser heating problems.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks An efficient boundary-type meshfree method for analysis of two-dimensional laser heating problems

Reference 27

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Observation 38035dbe-7cea-4301-b595-cda1339b60b4 · outbound

This paper cites Numerical prediction of fluid flow and heat transfer in welding with a moving heat source.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Numerical prediction of fluid flow and heat transfer in welding with a moving heat source

Reference 28

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Source-reported events for the cited work

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Observation 392df2d3-5392-495b-989e-7937ab8b1567 · outbound

This paper cites The partition-of-unity method for linear diffusion and convection problems: Accuracy, stabilization and multiscale interpretation.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks The partition-of-unity method for linear diffusion and convection problems: Accuracy, stabilization and multiscale interpretation

Reference 29

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Observation 8e246f36-b18d-4a85-a83f-246d31039e77 · outbound

This paper cites Parametric deep energy approach for elasticity accounting for strain gradient effects.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Parametric deep energy approach for elasticity accounting for strain gradient effects

Reference 30

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Observation 4b471bfd-3cbb-401e-aae0-104c128410ce · outbound

This paper cites Generalized finite element analysis of three-dimensional heat transfer problems exhibiting sharp thermal gradients.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Generalized finite element analysis of three-dimensional heat transfer problems exhibiting sharp thermal gradients

Reference 31

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Source-reported events for the cited work

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

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Observation dd4cbed9-09cf-40c1-bacc-f20a78d644d0 · outbound

This paper cites A paradigm for data-driven predictive modeling using field inversion and machine learning.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks A paradigm for data-driven predictive modeling using field inversion and machine learning

Reference 32

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation 9bbda590-0040-45af-851f-efaba474274c · outbound

This paper cites Automatic differentiation in pytorch.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Automatic differentiation in pytorch

Reference 33

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Source-reported events for the cited work

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Observation a44e4ace-852d-4d69-ab0f-1b477d17443b · outbound

This paper cites Adaptive physics-informed neural networks for dynamic coupled thermo- mechanical problems in large-size-ratio functionally graded materials.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Adaptive physics-informed neural networks for dynamic coupled thermo- mechanical problems in large-size-ratio functionally graded materials

Reference 34

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verified fuzzy
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Source-reported events for the cited work

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source=pdf_text observed=2026-08-15T19:06:47.941255Z digest=sha256:234c8b3dcb3e9fb09c262f2251a3769e44f76e04630489c64bc9e3fb18ccf1f9

Observation 2f196656-b274-4f1b-9dd4-8c715bf9972b · outbound

This paper cites Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems

Reference 35

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Observation e88ac2a8-6830-44a0-8e7e-5b7c5216db69 · outbound

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

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial dif- ferential equations

Reference 36

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Observation 1b1f6ef9-3c8c-4d98-827b-f423d7676b6d · outbound

This paper cites SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs

Reference 37

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Observation 251b2040-e0f7-44cb-af57-c90a9618622f · outbound

This paper cites Two-dimensional numerical simu- lation of heat transfer with moving heat source in welding using the Finite Pointset Method.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Two-dimensional numerical simu- lation of heat transfer with moving heat source in welding using the Finite Pointset Method

Reference 38

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Observation c51dab12-553c-4e6e-83b8-a0c02b669ad0 · outbound

This paper cites Mathematical theory of heat distribution during welding and cutting, aw s.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Mathematical theory of heat distribution during welding and cutting, aw s

Reference 39

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source=pdf_text observed=2026-08-15T19:06:47.962346Z digest=sha256:936df5db78aa9ae2a35c8b44793579ee136f3e5704ff0a86ef246e244d1b01e2

Observation 34ecd48b-8b42-4afd-b348-bf9b3590674e · outbound

This paper cites An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

Reference 40

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source=pdf_text observed=2026-08-15T19:06:47.966156Z digest=sha256:2fb43d9c539f9576d817faf2f7a6bb7236c684455ed5ddf15d91313a276b4628

Observation 47a46902-2701-45dd-8ee7-166a177d7606 · outbound

This paper cites Advances in computational mod- eling for laser powder bed fusion additive manufacturing: A comprehensive review of finite element techniques and strategies.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Advances in computational mod- eling for laser powder bed fusion additive manufacturing: A comprehensive review of finite element techniques and strategies

Reference 41

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source=pdf_text observed=2026-08-15T19:06:47.969723Z digest=sha256:369340b34adae6364e93c9ca86add021b7b1dcfd44560b53289d34d3e8c9bfe5

Observation cacbc523-2949-4fd2-be1e-ad2c845c33f4 · outbound

This paper cites On the performance of a Chimera-FEM implementation to treat moving heat sources and moving boundaries in time- dependent problems.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks On the performance of a Chimera-FEM implementation to treat moving heat sources and moving boundaries in time- dependent problems

Reference 42

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source=pdf_text observed=2026-08-15T19:06:47.973003Z digest=sha256:3ef2641f3a97eba24d78fe90b8f5f8aa23a91e5e9e2000f6bba836cab3f1d967

Observation 4613eeca-a5e7-4649-9f45-8af47611beb2 · outbound

This paper cites An Extrinsic Approach Based on Physics- Informed Neural Networks for PDEs on Surfaces.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks An Extrinsic Approach Based on Physics- Informed Neural Networks for PDEs on Surfaces

Reference 43

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-15T19:06:47.976504Z digest=sha256:f460a0c4652fcadfcb544bb7ee3b04774e09a745c1a4dfcb24a10fb5c06a3067

Observation 5c86f71d-1cd3-4277-a7c9-6a32c4714a65 · outbound

This paper cites Artificial intelligence for partial differential equations in computational me- chanics: A review.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Artificial intelligence for partial differential equations in computational me- chanics: A review

Reference 44

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source=pdf_text observed=2026-08-15T19:06:47.980401Z digest=sha256:fd44fccc6c0f751047adb3bcfc57a3aca18378b7ad02a31da7e87d84eb7cfe4a

Observation 91149b9d-47d8-4be2-ae45-b9ab8f5ebb18 · outbound

This paper cites Isogeometric boundary element method for steady-state heat transfer with concentrated/surface heat sources.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Isogeometric boundary element method for steady-state heat transfer with concentrated/surface heat sources

Reference 45

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source=pdf_text observed=2026-08-15T19:06:47.983950Z digest=sha256:6c32104d30d8324e6b4951e208aec8598b0eaccef3f8dfb8740061fc2bb78945

Observation 39ba05bd-74cc-483a-a75e-d72979d9c55f · outbound

This paper cites Multi-domain physics-informed neural networks for solving transient heat conduction problems in multilayer materials.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Multi-domain physics-informed neural networks for solving transient heat conduction problems in multilayer materials

Reference 46

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raw_fallback, observed 2026-08-15T19:06:48.532239Z

Source-reported events for the cited work

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

source=pdf_text observed=2026-08-15T19:06:47.987396Z digest=sha256:7ca2a6f1e5af810adc03144da3c6310452f27f6359b1c42be46cc3947231e41a

Observation b80a4a38-5a4c-4149-9291-77da89dd9354 · outbound

This paper cites A Comprehensive Survey on Transfer Learning.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks A Comprehensive Survey on Transfer Learning

Reference 47

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source=pdf_text observed=2026-08-15T19:06:47.991058Z digest=sha256:e13b93eac1a77fb22d35dce696a38fe7bae32ee4beb8b765bdb629de93165453

Observation 5e086aa1-a85b-4010-b120-151a87ab8328 · outbound

This paper cites Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning

Reference 48

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source=pdf_text observed=2026-08-15T19:06:47.994755Z digest=sha256:cc34daa73434d541f5a0f94a735f911f545a2264dd51ea6a162d18151d7fc34e

Observation 61601e71-a59f-48f6-aecc-8fdcf4f248a4 · outbound

This paper cites org / 10.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks org / 10

Reference 9310

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source=pdf_text observed=2026-08-15T19:06:47.958924Z digest=sha256:e7cf6527136f035cbb84a0d7b1d7d8c4e7090dd2ad04ad531003524681b10ff6

Pith citing papers

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