Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks? | Paper Citation Record

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.313291Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.203984Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.220687Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.233272Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.283141Z

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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

Resolution: malformed identifier; raw_fallback, observed 2026-08-11T00:55:36.270615Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.294753Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.308739Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.312942Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.259215Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.352642Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-11T00:55:34.375141Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.240639Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.228487Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.215698Z

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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

Resolution: verified exact; doi, observed 2026-08-11T00:55:35.183583Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.193940Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.181590Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.169509Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.157563Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.145464Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.121869Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:55:36.101208Z

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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

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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

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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

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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

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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

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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

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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

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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

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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

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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

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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

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