Paper Citation Record · LEDGER

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks

As of 18 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 1 inbound Pith citation observation for arXiv:2505.07311.

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

pith.paper-citation-record.v1
2505.07311 v1

Coverage vector

measured 50 of 50 reference resolution

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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

Source: pith, observed 2026-08-15T16:44:53.963226Z

Reference resolution

50 of 50 outbound references displayed

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External citation measurements

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Outbound references

Observation 5339a5f5-c814-41fe-a8a9-403dc4b103f9 · outbound

This paper cites Physical activation functions (PAFs): An ap- proachformoreefficientinductionofphysicsintophysics-informedneuralnetworks(PINNs).

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Physical activation functions (PAFs): An ap- proachformoreefficientinductionofphysicsintophysics-informedneuralnetworks(PINNs)

Reference 1

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This paper cites A novel framework for policy mirror descent with general parameterization and linear convergence.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks A novel framework for policy mirror descent with general parameterization and linear convergence

Reference 2

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This paper cites Fine-grained analysis of optimization and generalization for overpa- rameterized two-layer neural networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Fine-grained analysis of optimization and generalization for overpa- rameterized two-layer neural networks

Reference 3

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This paper cites Learning theory from first principles.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Learning theory from first principles

Reference 4

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This paper cites Rademacher and Gaussian Complexities: Risk Bounds and Structural Results.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Rademacher and Gaussian Complexities: Risk Bounds and Structural Results

Reference 5

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Observation b6ca3c0b-e682-41f6-8c57-99afdb7b83ca · outbound

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

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Three ways to solve partial differential equations with neural networks—A review

Reference 6

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Observation 81d44f6b-30af-47df-ac2e-68094338c92b · outbound

This paper cites Finite element methods of least-squares type.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Finite element methods of least-squares type

Reference 7

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Observation 8e815b1a-d62e-4f30-9e78-75d26e53747e · outbound

This paper cites The Challenges of the Nonlinear Regime for Physics-Informed Neural Networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks The Challenges of the Nonlinear Regime for Physics-Informed Neural Networks

Reference 8

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Observation 62be19cd-c4dd-48df-ac67-c5dc16d5cef4 · outbound

This paper cites Concentration inequalities.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Concentration inequalities

Reference 9

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Observation 6938390b-bd9a-47bb-9fab-70bca809ea73 · outbound

This paper cites On the Spectral Bias of Neural Networks in the Neural Tangent Kernel Regime.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks On the Spectral Bias of Neural Networks in the Neural Tangent Kernel Regime

Reference 10

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Observation 319052ca-25c4-44b1-b21f-2ee5c7c09a6d · outbound

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

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Physics-informed neural networks (PINNs) for fluid mechanics: A re- view

Reference 11

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Observation d30ad5d9-35f0-4083-a4f5-2f61fa56e842 · outbound

This paper cites Sample Complexity and Overparameterization Bounds for Temporal- Difference Learning With Neural Network Approximation.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Sample Complexity and Overparameterization Bounds for Temporal- Difference Learning With Neural Network Approximation

Reference 12

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This paper cites On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport

Reference 13

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Observation bc0fbe33-cb9c-4e9c-add6-e64847da35f9 · outbound

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

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Scientific machine learning through physics–informed neural net- works: Where we are and what’s next

Reference 14

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Observation 68887062-3f38-4e62-b9b9-f485a6eaad61 · outbound

This paper cites Error estimates for physics- informed neural networks approximating the Navier–Stokes equations.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Error estimates for physics- informed neural networks approximating the Navier–Stokes equations

Reference 15

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Observation 116f8c0e-73a1-4f71-81b9-aa6ed953ba76 · outbound

This paper cites Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs

Reference 16

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Observation c3fe407f-6502-4034-8e3b-7474b7dc0865 · outbound

This paper cites Gradient descent finds global minima of deep neural networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Gradient descent finds global minima of deep neural networks

Reference 17

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This paper cites Gradient Descent Provably Optimizes Over-parameterized Neural Networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Gradient Descent Provably Optimizes Over-parameterized Neural Networks

Reference 18

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This paper cites AlgorithmsforsolvinghighdimensionalPDEs: from nonlinear Monte Carlo to machine learning.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks AlgorithmsforsolvinghighdimensionalPDEs: from nonlinear Monte Carlo to machine learning

Reference 19

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Unresolved cited work

Reference 20

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This paper cites Gradient descent finds the global optima of two- layerphysics-informedneuralnetworks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Gradient descent finds the global optima of two- layerphysics-informedneuralnetworks

Reference 21

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This paper cites An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning

Reference 22

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Elliptic problems in nonsmooth domains

Reference 23

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Observation d3f6e3ca-a854-414a-913c-88e7c3277007 · outbound

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Neural tangent kernel: Convergence and generalization in neural networks

Reference 24

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This paper cites Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks

Reference 25

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Observation 9a716d7c-975c-47fb-8cfa-1ce0b32d6745 · outbound

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Neural tangent kernels, transportation mappings, and universal approximation

Reference 26

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Observation b9abb0e4-30aa-4dca-9e25-09bca19dd75c · outbound

This paper cites DRM Revisited: A Complete Error Analysis.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks DRM Revisited: A Complete Error Analysis

Reference 27

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Physics-informed machine learning

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This paper cites PINNACLE: PINN Adaptive ColLocation and Experimen- talpointsselection.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks PINNACLE: PINN Adaptive ColLocation and Experimen- talpointsselection

Reference 29

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Observation 51fedfa5-2ecf-4eb4-9ffa-971dc3d5ec22 · outbound

This paper cites Probability in Banach Spaces: Isoperimetry and Processes.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Probability in Banach Spaces: Isoperimetry and Processes

Reference 30

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This paper cites Chapter 11 - Two-layer neural networks for partial differential equations: optimization and generalization theory.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Chapter 11 - Two-layer neural networks for partial differential equations: optimization and generalization theory

Reference 31

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Observation 0a0f2be9-7e57-48cd-a5e2-150781415026 · outbound

This paper cites Influence of Activation Functions on the Conver- gence of Physics-Informed Neural Networks for 1D Wave Equation.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Influence of Activation Functions on the Conver- gence of Physics-Informed Neural Networks for 1D Wave Equation

Reference 32

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks On the method of bounded differences

Reference 33

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Observation 32daa8e7-370d-48cd-a348-5cba183fe957 · outbound

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Estimatesonthegeneralizationerrorofphysics- informed neural networks for approximating PDEs

Reference 34

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This paper cites Notes on Exact Boundary Values in Residual Minimisation.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Notes on Exact Boundary Values in Residual Minimisation

Reference 35

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Observation abe012aa-82bd-4d62-8c11-48558639a238 · outbound

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Random features for large-scale kernel machines

Reference 36

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Observation cb7cc3f7-5283-4735-a774-05a05ca4e0e0 · outbound

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Uniform approximation of functions with random bases

Reference 37

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

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Physics-informed neural net- works: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 38

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Observation 78040e3a-8898-4090-bb0b-833637bc2538 · outbound

This paper cites Challenges in Training PINNs: A Loss Landscape Perspective.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Challenges in Training PINNs: A Loss Landscape Perspective

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:34:57.924583Z

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Observation 114f9861-214e-4c92-a921-603ccce9fd89 · outbound

This paper cites DGM: A deep learning algorithm for solving partial differential equations.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks DGM: A deep learning algorithm for solving partial differential equations

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:34:57.909516Z

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Observation 805daaba-6056-4179-815a-a5ddffb9a87f · outbound

This paper cites Deep learning theory (DRAFT).

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Deep learning theory (DRAFT)

Reference 41

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Observation 7dfcee9e-c19b-452c-a6f8-c8eba9891f1e · outbound

This paper cites From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning

Reference 42

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Observation 29a48a2f-f032-4956-851a-8e1c66c5e5d3 · outbound

This paper cites Learning Specialized Activation Functions for Physics-Informed Neu- ral Networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Learning Specialized Activation Functions for Physics-Informed Neu- ral Networks

Reference 43

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Observation f59276ea-2af7-4031-9363-e0599d1f7c4e · outbound

This paper cites An Expert's Guide to Training Physics-informed Neural Networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks An Expert's Guide to Training Physics-informed Neural Networks

Reference 44

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Observation 17392fd5-aae9-4dca-9f1f-f9ea501e75c2 · outbound

This paper cites Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networks

Reference 45

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Observation 1dbf21d8-47d4-47c5-9f22-f1b84615ac6f · outbound

This paper cites Convergence Analysis of Natural Gradient Descent for Over-parameterized Physics-Informed Neural Networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Convergence Analysis of Natural Gradient Descent for Over-parameterized Physics-Informed Neural Networks

Reference 46

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Observation 264c7b08-af4d-4d00-9aa6-02a02ab1fe73 · outbound

This paper cites A Unified Framework for the Error Analysis of Physics-Informed Neural Networks.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks A Unified Framework for the Error Analysis of Physics-Informed Neural Networks

Reference 47

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Observation c42fca29-8305-4774-81d1-45285edad674 · outbound

This paper cites Feature Mapping in Physics-Informed Neural Networks (PINNs).

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Feature Mapping in Physics-Informed Neural Networks (PINNs)

Reference 48

Resolution: verified exact; local_arxiv, observed 2026-08-15T22:34:57.568409Z

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Observation 1fefbf67-1d86-42ed-b1e1-e44217e7000c · outbound

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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Unresolved cited work

Reference 240

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9cc57bbd-a782-4b06-9207-21aeac06b86b · outbound

This paper cites an unresolved cited work.

Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks Unresolved cited work

Reference 2024

Resolution: unresolved; raw_fallback, observed 2026-08-15T22:34:58.100614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation 87511850-c194-4e87-9c89-56a876c50cfc · inbound

Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation cites this paper.

Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:44:53.968550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.