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Paper Citation Record · LEDGER

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?

As of 15 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 1 inbound Pith citation observation for arXiv:2412.19235.

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

pith.paper-citation-record.v1
2412.19235 v1

Coverage vector

measured 62 of 62 reference resolution

Typed states for the displayed outbound observations.

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measured 63 of 63 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 2026-08-10T23:15:24.634970Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T23:15:24.724388Z

Reference resolution

62 of 62 outbound references displayed

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External citation measurements

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Outbound references

Observation c5a4c5bb-3fa1-4dac-a8cd-83e59cfe5e26 · outbound

This paper cites Highly accurate protein structure prediction with AlphaFold,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Highly accurate protein structure prediction with AlphaFold,

Reference 1

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Observation 1585db19-ccab-4d02-bfc1-1eb1b0c8f316 · outbound

This paper cites A Foundation Model for the Earth System.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? A Foundation Model for the Earth System

Reference 2

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Observation 6729ca3b-59d2-47c7-a05b-630c69bae62e · outbound

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

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

Reference 3

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Observation aa1c78e7-c1f2-48cf-b7bf-eb4b6a2b3782 · outbound

This paper cites Respecting causality is all you need for training physics-informed neural networks.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Respecting causality is all you need for training physics-informed neural networks

Reference 4

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Observation e9d6ae48-0881-4256-b76d-4fdb4584d08b · outbound

This paper cites A Modified Physics Informed Neural Networks for Solving the Partial Differential Equation with Conservation Laws,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? A Modified Physics Informed Neural Networks for Solving the Partial Differential Equation with Conservation Laws,

Reference 5

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation d6182e3d-9d08-4c67-9e59-20987c4d7125 · outbound

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

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,

Reference 6

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Observation 61b5e6e0-0d00-42ed-a5cb-a9cedd965a55 · outbound

This paper cites A General Neural- Networks-Based Method for Identification of Partial Differential Equations, Implemented on a Novel AI Accelerator,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? A General Neural- Networks-Based Method for Identification of Partial Differential Equations, Implemented on a Novel AI Accelerator,

Reference 7

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Observation e57a5618-1d00-4de9-b16c-a7d8daa9afb5 · outbound

This paper cites Spectral Neural Operators.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Spectral Neural Operators

Reference 8

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Observation 8d860109-59eb-45fa-9636-aef04b1304f6 · outbound

This paper cites Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 9

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Observation 7f2d591b-cac5-48b4-a4ee-d5704b89c266 · outbound

This paper cites About optimal loss function for training physics-informed neural networks under respecting causality.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? About optimal loss function for training physics-informed neural networks under respecting causality

Reference 10

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Observation 404839b9-5a3b-4f71-9efd-40f5e7c01855 · outbound

This paper cites A hybrid neural network-first principles approach to process modeling,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? A hybrid neural network-first principles approach to process modeling,

Reference 11

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 6cc145ce-38b2-44bb-bb85-29d40c6e8f5d · outbound

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

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Artificial neural networks for solving ordinary and partial differential equations,

Reference 12

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation a82a6cb1-5bc0-4c33-87a8-2e6d59a3a8f2 · outbound

This paper cites A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations,

Reference 13

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Observation ed93216c-4bee-424d-b113-d4525bc82c70 · outbound

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

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? hp-VPINNs: Variational physics-informed neural networks with domain decomposition,

Reference 14

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Observation 34da14bc-d165-46f1-b0f4-91d7b3cbad09 · outbound

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

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data,

Reference 15

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Observation d504ecf0-0d4a-404a-9471-9306e04839a5 · outbound

This paper cites Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

Reference 16

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Observation a3ca869f-ad92-484b-a0f6-b7ccc75b30ec · outbound

This paper cites Thermodynamically consistent physics-informed neural networks for hyperbolic systems,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Thermodynamically consistent physics-informed neural networks for hyperbolic systems,

Reference 17

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Observation fd3d5f20-b38b-4cd6-91b9-7f8594c8c6ec · outbound

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

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Physics-informed neural networks (PINNs) for fluid mechanics: a review,

Reference 18

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Observation a5856965-37fc-499c-8baf-a1f012e1eaad · outbound

This paper cites Solving the wave equation with physics-informed deep learning.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Solving the wave equation with physics-informed deep learning

Reference 19

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Observation ea31aa55-9f15-4dda-9f34-888a936d1cd2 · outbound

This paper cites Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport,

Reference 20

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 0ec77518-a373-4e78-93c0-2f9343b4a814 · outbound

This paper cites AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification

Reference 21

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Observation d8479803-0037-4742-8a4b-0e3f7d44bb20 · outbound

This paper cites PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks

Reference 22

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Observation 16707c9e-18d4-4b7d-8241-0dfc7901bb7d · outbound

This paper cites Element-wise multiplication based deeper physics-informed neural networks,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Element-wise multiplication based deeper physics-informed neural networks,

Reference 23

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Observation 3e0f5fb9-10c0-4635-8ba3-f61f54ee8ad6 · outbound

This paper cites Multilayer feedforward networks are universal approximators,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Multilayer feedforward networks are universal approximators,

Reference 24

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Observation 3e69b1e5-fa9f-4910-b4d3-032c2a736b44 · outbound

This paper cites Approximation by superpositions of a sigmoidal function,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Approximation by superpositions of a sigmoidal function,

Reference 25

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Observation f0c4a884-b9bc-4f88-acf7-119a37abb1b5 · outbound

This paper cites Error bounds for approximations with deep relu networks,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Error bounds for approximations with deep relu networks,

Reference 26

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Observation 0df13877-9aae-4ac4-a0aa-e952a255ce6f · outbound

This paper cites On functions of three variables,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? On functions of three variables,

Reference 27

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Observation accb6bae-e5d9-483c-96e8-c2a073dc4066 · outbound

This paper cites On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition,

Reference 28

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Observation 0e770366-db0d-49b6-9553-64cc8a4659e1 · outbound

This paper cites On the representation of continuous functions of several variables by superposition of continuous functions of a smaller number of variables,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? On the representation of continuous functions of several variables by superposition of continuous functions of a smaller number of variables,

Reference 29

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation eb7a909c-127a-48b7-af09-bccfab16ff3f · outbound

This paper cites Lower bounds for approximation by mlp neural networks,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Lower bounds for approximation by mlp neural networks,

Reference 30

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 670e8e04-3c9a-45a5-a5cd-7e43e394a81a · outbound

This paper cites Approximation capability of two hidden layer feedforward neural networks with fixed weights,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Approximation capability of two hidden layer feedforward neural networks with fixed weights,

Reference 31

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Observation 5e508921-46ea-4168-98ba-1928607db53f · outbound

This paper cites Nonlinear approximation via compositions,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Nonlinear approximation via compositions,

Reference 32

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 3d502543-f90f-45bc-8584-f53415add897 · outbound

This paper cites Neural network approximation: Three hidden layers are enough,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Neural network approximation: Three hidden layers are enough,

Reference 33

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation c0dfc51b-ad73-4c46-b2ee-74edc6120885 · outbound

This paper cites Griewank and A.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Griewank and A

Reference 34

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation a537311d-ac46-4b5d-a3cc-267bc19479dd · outbound

This paper cites Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks,

Reference 35

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.608780Z digest=sha256:24cc182bf8126ce0828730e72b2b5ec10e1c7373a91ed0ddf97aab5cca113365

Observation 5931973b-9263-433b-80e8-a53310945c44 · outbound

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

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? When and why PINNs fail to train: A neural tangent kernel perspective,

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:36.087436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.626612Z digest=sha256:e214300e14f6297b43c607904edb2f76824cddde17db07a9bc0a8628fd6cfac4

Observation a18b9fe2-14ad-4dab-b296-56e45ae728aa · outbound

This paper cites Physics-informed radial basis network (pirbn): A local approximating neural network for solving nonlinear partial differential equations,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Physics-informed radial basis network (pirbn): A local approximating neural network for solving nonlinear partial differential equations,

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.630913Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.630913Z digest=sha256:7b8e0343ca157ca26fcae5fed1b68f0684fd0d368b8892d68fc5456b8e4b7118

Observation 38fed2a4-94e5-4bf9-9415-2b29bec15c1e · outbound

This paper cites Understanding the difficulty of training deep feedforward neural networks,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Understanding the difficulty of training deep feedforward neural networks,

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:36.074254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.638046Z digest=sha256:d1510a94fef2147ad7184b997995cd38f199afa2f43758d3cdf1e99a0f522c6b

Observation 2a97f22c-366c-414e-b6ba-fcfbe3100eab · outbound

This paper cites Paszke, S.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Paszke, S

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:36.053997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.644878Z digest=sha256:ca05be55ea2a77635194f1fa7ad02000cb79bb29665b2685d1809bc097256dee

Observation f7a1c782-debe-4d46-8b99-5546c6c7e820 · outbound

This paper cites Available: https://doi.org/10.1137/20M1318043.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Available: https://doi.org/10.1137/20M1318043

Reference 40

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.612801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.612801Z digest=sha256:ff7c2293df0cba96595ef8a52e7e6e693a0b2d17d53e0f813345b408887f418c

Observation 761cd7b6-936d-4180-8599-50c0280199c0 · outbound

This paper cites Relativistic slingshot: A source for single circularly polarized attosecond x-ray pulses,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Relativistic slingshot: A source for single circularly polarized attosecond x-ray pulses,

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.667324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.667324Z digest=sha256:93d247e1a823f27bcdfc9da1f7e985af9286e15c69cdcd5dde2397c08248a32a

Observation fc1f43df-de9d-4140-905d-69bb59343086 · outbound

This paper cites Deterministic nonperiodic flow,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Deterministic nonperiodic flow,

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:36.042104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.672939Z digest=sha256:54ac71182c6f241218acf70bc6e7170455eea952be82c03503cc70dc0d49e359

Observation ced835e8-5735-4217-a0e0-349423659fdd · outbound

This paper cites Separable Physics-Informed Neural Networks.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Separable Physics-Informed Neural Networks

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.694850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.694850Z digest=sha256:0415d90aaa9c0a3b5dfd0368d9ef3b55d9dc0650b53082934e5aa4db1c755049

Observation ea8816b1-92e8-4c11-b33a-5ce6ef23182e · outbound

This paper cites Separable Physics-Informed Neural Networks for the solution of elasticity problems.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Separable Physics-Informed Neural Networks for the solution of elasticity problems

Reference 44

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.734744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.734744Z digest=sha256:03ffac3ecfbdec098ac3f782bceb41fe6701a5fc8c723d99ef5f18d63e6efa64

Observation 74ca8f62-a006-4786-b729-41abbaaf0a0e · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Adam: A Method for Stochastic Optimization

Reference 45

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.656487Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.656487Z digest=sha256:c6f123acc3cff4ec7451cd37e1e41fcbb674bce388f5d9a6c736fdaa23854406

Observation 71a134f5-9478-437c-b500-088b7a02f0ae · outbound

This paper cites Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.794748Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.794748Z digest=sha256:b5c533cf3030e6842ad1d8eddb813bd92f4f088767709c6e28e090d8064c8bb0

Observation 31d9d4dd-f970-4fb5-a508-27c7763e2895 · outbound

This paper cites Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.824876Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.824876Z digest=sha256:cfd15aaba1ce73048a723b8a9475228f542be066805a1276d7fa5b5bf4c930e7

Observation 0740c961-9510-45a2-80e1-28dba623c6b6 · outbound

This paper cites A novel sequential method to train physics informed neural networks for Allen–Cahn and Cahn–Hilliard equations,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? A novel sequential method to train physics informed neural networks for Allen–Cahn and Cahn–Hilliard equations,

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:36.016027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.839027Z digest=sha256:4244f4e44bfa2a0c453abf4dc313fb76681d8b68993025eda3a45475ff071e0b

Observation abdbc23e-d712-4995-ab88-ffdea28ef3d8 · outbound

This paper cites Dasa-Pinns: Differentiable Adversarial Self-Adaptive Pointwise Weighting Scheme for Physics-Informed Neural Networks,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Dasa-Pinns: Differentiable Adversarial Self-Adaptive Pointwise Weighting Scheme for Physics-Informed Neural Networks,

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:36.002908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.843834Z digest=sha256:454cd5b84c6171feeede877a48dbc261226947810b1183c0d75678fa540898ff

Observation 4f980d00-44f2-467a-a4f4-eff9f437af1e · outbound

This paper cites an unresolved cited work.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:55:36.029997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.761381Z digest=sha256:068cc5d0402d806cb41228b2d99ae6265ca0fab53e5edac2106469806a4a9206

Observation 22f51944-ae08-4d9b-820a-a2b28eaaacdc · outbound

This paper cites Physics informed extreme learning machine (pielm)–a rapid method for the numerical solution of partial differential equations,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Physics informed extreme learning machine (pielm)–a rapid method for the numerical solution of partial differential equations,

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:35.977833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.859746Z digest=sha256:6b37db0e5e0f8738f291388a78fe08e510da16591e169193a535cd1e14242cce

Observation 15432256-1c59-412d-ad1d-4dbe29c20cbb · outbound

This paper cites Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations,

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:35.967243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.864521Z digest=sha256:edf0ee559a38441255121500cfd50dcbc38eb529075ecf60cbbe0f32201f5640

Observation b641d23f-a81d-42c5-90b8-133d7323e856 · outbound

This paper cites Extreme learning machines: a survey,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Extreme learning machines: a survey,

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:35.954617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.879352Z digest=sha256:1f1e924491b0a3693bb1d4e954f3ed12099d393036dbe6d2afbf2414a510375c

Observation e9c5dbc4-f4e5-414b-a27b-e9f9673d0912 · outbound

This paper cites A Nonoverlapping Domain Decomposition Method for Extreme Learning Machines: Elliptic Problems.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? A Nonoverlapping Domain Decomposition Method for Extreme Learning Machines: Elliptic Problems

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.914750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.914750Z digest=sha256:3ed32a26a69a75aeb495990658ce97ac30f8b5268fcf39cc580370bc9e1bea34

Observation 7da05908-2583-4bb7-9943-84fa954fdf4c · outbound

This paper cites Extreme learning machine: Theory and applications,.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Extreme learning machine: Theory and applications,

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:35.989507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.850668Z digest=sha256:7cdb034e4154c3f28d0fac30a49b7a2b124490fe2fefb215509d9fc6f2d2b4d5

Observation 3eb8dd78-d9bd-426f-9ca1-b10cebb2c0c7 · outbound

This paper cites HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks

Reference 56

Resolution
verified exact
local_arxiv, observed 2026-08-11T00:55:35.237881Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.970859Z digest=sha256:4ac1b78d24a6127935b35fc4cc46dd7ad43628987b37fd28a0a1d7f0108600a4

Observation 00e63e99-ea79-47e9-8ee8-4d185afbe78f · outbound

This paper cites Parameterized Physics-informed Neural Networks for Parameterized PDEs.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Parameterized Physics-informed Neural Networks for Parameterized PDEs

Reference 57

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.985532Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.985532Z digest=sha256:a654bd15f3786271700f0b7f9e403d652443e553c61226aebdee67c1e1e84d6b

Observation 73be9df3-a89b-4c72-b867-0ef2d7e86e9f · outbound

This paper cites Residual-based attention and connection to information bottleneck theory in PINNs.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Residual-based attention and connection to information bottleneck theory in PINNs

Reference 60

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.939883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.939883Z digest=sha256:45a424902af1a959a195b4aa58f8cd6e3cea77736e16c000f430cb7ee28cfcc8

Observation a59d9fa5-5675-4665-ae48-e89a9646c012 · outbound

This paper cites Available: https://epubs.siam.org/doi/abs/10.1137/1.9780898717761.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Available: https://epubs.siam.org/doi/abs/10.1137/1.9780898717761

Reference 2008

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.602104Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.602104Z digest=sha256:259c4d2656c9c4be8804022b4745dc786e049ad739fbbb4579331838d714f735

Observation e3683708-e29b-400e-8249-ef415ecb2b00 · outbound

This paper cites Available: https://api.semanticscholar.org/CorpusID:225076123.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Available: https://api.semanticscholar.org/CorpusID:225076123

Reference 2020

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:55:36.132620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T00:55:34.593579Z digest=sha256:fb7e2ded7d4fc42da691fcca8b766a009cc59fcbd746c05e601bade521eedbf4

Observation 148db77d-c408-4ded-b7e2-72f4be53f5e0 · outbound

This paper cites Available: https://doi.org/10.1038%2Fs42256-021-00302-5.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Available: https://doi.org/10.1038%2Fs42256-021-00302-5

Reference 2021

Resolution
malformed identifier
no resolver link, observed 2026-08-11T00:55:34.207903Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.207903Z digest=sha256:3fef16b2a9452e8280c4d32c7db5f78de0c2944a40cf2b0144a8b4b1c2209c97

Observation 2438379d-c831-4733-ae1f-c1b2dee2334d · outbound

This paper cites Element-wise Multiplication Based Deeper Physics-Informed Neural Networks.

Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? Element-wise Multiplication Based Deeper Physics-Informed Neural Networks

Reference 2024

Resolution
unresolved
no resolver link, observed 2026-08-11T00:55:34.366020Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:55:34.366020Z digest=sha256:b6a1262b9b0e2c59c62c699bfa44d293553eec57067ec89752ac318528ce4d2e

Pith citing papers

Observation 6b238d38-48d2-4072-9b14-c7740ca96684 · inbound

About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks cites this paper.

About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?

Reference 21

Resolution
verified exact
local_arxiv, observed 2026-08-10T23:15:24.728068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T23:15:24.634970Z digest=sha256:75233a3b3041ca1dff7d9a9e466b8c8108f5545892ad033a0d45cf3a10b8083b