Paper Citation Record · LEDGER

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks

As of 11 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 2 inbound Pith citation observations for arXiv:2501.02762.

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

pith.paper-citation-record.v1
2501.02762 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

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One-hop event checks from named stored sources.

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measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:23:21.069062Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T03:30:50.408827Z

Reference resolution

45 of 45 outbound references displayed

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External citation measurements

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Outbound references

Observation f29ec767-8e0b-4e75-82ee-81f9fd2f3630 · outbound

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

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 1

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Observation a071679a-c23a-406c-b587-771907de4930 · outbound

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

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-informed neural networks (pinns) for fluid mechanics: A review

Reference 2

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Observation 1c9068a9-94ea-44f4-a9e9-a888a3a53ee3 · outbound

This paper cites Physics-informed neural networks with periodic activation functions for solute transport in heterogeneous porous media.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-informed neural networks with periodic activation functions for solute transport in heterogeneous porous media

Reference 3

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Observation d9980c23-b274-4d5a-bab5-fae47ae3a9e0 · outbound

This paper cites Physics-informed neural networks (pinn) for computational solid mechanics: Numerical frameworks and applications.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-informed neural networks (pinn) for computational solid mechanics: Numerical frameworks and applications

Reference 4

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Observation 567798be-024c-4bbf-8584-7a0368bb9ffc · outbound

This paper cites A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations

Reference 5

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Observation 4d3c4a9d-9e3a-4aaa-9fcc-f3fbc8143205 · outbound

This paper cites Enhancing Arterial Blood Flow Simulations through Physics-Informed Neural Networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Enhancing Arterial Blood Flow Simulations through Physics-Informed Neural Networks

Reference 6

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Observation 441e3b16-3c14-4a65-90f0-e08a7ac1ca19 · outbound

This paper cites Physics-informed neural network estimation of material properties in soft tissue nonlinear biomechanical models.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-informed neural network estimation of material properties in soft tissue nonlinear biomechanical models

Reference 7

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Observation 52c03abe-1f93-4e6b-9d1c-fbfaa77c80f4 · outbound

This paper cites A physics-informed neural network to model the flow of dry particles.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks A physics-informed neural network to model the flow of dry particles

Reference 8

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Observation ed2788bc-ff44-45d4-8b1e-48767a4946c0 · outbound

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

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning

Reference 9

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Observation fed351c4-0e35-4341-a356-a92bbb406644 · outbound

This paper cites Physics-guided, physics-informed, and physics-encoded neural networks and operators in scientific com- puting: Fluid and solid mechanics.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-guided, physics-informed, and physics-encoded neural networks and operators in scientific com- puting: Fluid and solid mechanics

Reference 10

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Observation d1222e44-3c55-4a33-844a-137f11eca868 · outbound

This paper cites Physics-informed machine learning for modeling multidimensional dynamics.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-informed machine learning for modeling multidimensional dynamics

Reference 11

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Observation 8d9deea6-31e4-4930-a5f6-3d33ec8e9be5 · outbound

This paper cites Surrogate modeling of multi-dimensional premixed and non-premixed combustion using pseudo-time stepping physics-informed neural networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Surrogate modeling of multi-dimensional premixed and non-premixed combustion using pseudo-time stepping physics-informed neural networks

Reference 12

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Observation a37b265c-9504-4a91-a7bc-bd26577813bc · outbound

This paper cites Tackling the curse of dimensionality with physics-informed neural networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Tackling the curse of dimensionality with physics-informed neural networks

Reference 13

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Observation c6c7d5eb-c6ad-4f49-a49b-85911f2e374e · outbound

This paper cites Understanding and mitigating gradient pathologies in physics-informed neural networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Understanding and mitigating gradient pathologies in physics-informed neural networks

Reference 14

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Observation 0b2f08ff-58ba-45a9-8127-d602fdcaeb83 · outbound

This paper cites δ-pinns: physics-informed neural networks on complex geometries.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks δ-pinns: physics-informed neural networks on complex geometries

Reference 15

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Observation 08f05a04-f8de-4c48-bb39-2992a243ad58 · outbound

This paper cites Discontinuity computing using physics-informed neural networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Discontinuity computing using physics-informed neural networks

Reference 16

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Observation 0e3aa1a9-852f-4367-8fdb-c57a0ef156cb · outbound

This paper cites KAN 2.0: Kolmogorov-Arnold Networks Meet Science.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks KAN 2.0: Kolmogorov-Arnold Networks Meet Science

Reference 17

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Observation 9bb40ebf-a78f-4b81-a69e-712e1ef8ea68 · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks KAN: Kolmogorov-Arnold Networks

Reference 18

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Observation 6754c3ac-d6e6-4533-91b7-410b767fdb6f · outbound

This paper cites A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks

Reference 19

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Observation 9ed3ec71-555e-4fa3-a9bc-16a310016726 · outbound

This paper cites On a constructive proof of kolmogorov’s superposition theorem.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks On a constructive proof of kolmogorov’s superposition theorem

Reference 20

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Observation 1e0bdf77-c413-4af7-af4a-7f512ee5dd34 · outbound

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

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition

Reference 21

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Observation 05e906c2-b37e-4028-8c59-964887403593 · outbound

This paper cites Finite basis kolmogorov-arnold networks: domain decomposition for data-driven and physics-informed problems.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Finite basis kolmogorov-arnold networks: domain decomposition for data-driven and physics-informed problems

Reference 22

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Observation 7a0a64e7-6cce-4de2-a367-cbd85673d03a · outbound

This paper cites ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU

Reference 23

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Observation 1354e783-8230-41c3-844d-a3f4fd507867 · outbound

This paper cites KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics

Reference 24

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Observation 9726c31c-0912-466f-a1f1-b07fa087228a · outbound

This paper cites Kolmogorov-Arnold Networks are Radial Basis Function Networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Kolmogorov-Arnold Networks are Radial Basis Function Networks

Reference 25

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Observation 61af935a-3a65-4dd8-994c-2b38ba481151 · outbound

This paper cites Radial basis function neural network (rbfnn) approximation of cauchy inverse problems of the laplace equation.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Radial basis function neural network (rbfnn) approximation of cauchy inverse problems of the laplace equation

Reference 26

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Observation a603d7c3-22e7-40bd-b704-65addf3f6464 · outbound

This paper cites Wav-KAN: Wavelet Kolmogorov-Arnold Networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Wav-KAN: Wavelet Kolmogorov-Arnold Networks

Reference 27

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Observation 1423961f-cc70-4512-abc5-d7ab8ea3cc43 · outbound

This paper cites A novel growing wavelet neural network algorithm for solving chemotaxis systems with blow-up.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks A novel growing wavelet neural network algorithm for solving chemotaxis systems with blow-up

Reference 28

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Observation 670e877a-7591-4c1f-b4fb-0045f0d9fc53 · outbound

This paper cites Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

Reference 29

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Observation b3792ca4-46df-4447-a574-1a2a0de4d1b5 · outbound

This paper cites Control of a hydraulic generator regulating system using chebyshev-neural-network-based non-singular fast terminal sliding mode method.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Control of a hydraulic generator regulating system using chebyshev-neural-network-based non-singular fast terminal sliding mode method

Reference 30

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Observation a0304274-46b4-4907-a961-7eca0a29a507 · outbound

This paper cites Development of a novel activation function based on chebyshev polynomials: an aid for classification and denoising of images.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Development of a novel activation function based on chebyshev polynomials: an aid for classification and denoising of images

Reference 31

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Observation cfcfcf48-78bc-4671-8abf-f48c6d50c3c7 · outbound

This paper cites Physics-informed Kolmogorov-Arnold Network with Chebyshev Polynomials for Fluid Mechanics.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Physics-informed Kolmogorov-Arnold Network with Chebyshev Polynomials for Fluid Mechanics

Reference 32

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Observation 0bfaf39f-f04d-466b-bbc0-d9d4e2f98b26 · outbound

This paper cites EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials

Reference 33

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Observation a29842f8-e13d-4035-be44-654d4a9db679 · outbound

This paper cites Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks

Reference 34

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Observation d4ad3732-6315-4789-b32c-858931303b20 · outbound

This paper cites SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks

Reference 35

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This paper cites Partial differential equations , volume 19.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Partial differential equations , volume 19

Reference 36

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Observation 631e4752-81cf-4c21-8236-6f6b5f8860a2 · outbound

This paper cites Sur les probl` emes aux d´ eriv´ ees partielles et leur signification physique.Princeton university bulletin , pages 49–52, 1902.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Sur les probl` emes aux d´ eriv´ ees partielles et leur signification physique.Princeton university bulletin , pages 49–52, 1902

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:09:11.088957Z

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This paper cites Solutions of ill-posed problems.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Solutions of ill-posed problems

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:09:11.073795Z

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Observation 0768ecb3-f393-4510-8184-35462eac762f · outbound

This paper cites Deep learning, volume 1.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Deep learning, volume 1

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:09:11.057356Z

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Observation 56718516-d7da-49f8-9424-e4fee1df6124 · outbound

This paper cites Pattern recognition and machine learning , volume 4.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Pattern recognition and machine learning , volume 4

Reference 40

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This paper cites A brief review of feed-forward neural networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks A brief review of feed-forward neural networks

Reference 41

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Observation 8d01d7a8-38d5-4d7d-938f-db38162ebea1 · outbound

This paper cites Introduction to multi-layer feed-forward neural networks.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Introduction to multi-layer feed-forward neural networks

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:09:11.022298Z

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Observation 016e6288-4177-499b-a4b5-e67d18d3c3f2 · outbound

This paper cites Approximation by superpositions of a sigmoidal function.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Approximation by superpositions of a sigmoidal function

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:09:11.006707Z

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Observation e9328dbc-be48-4c85-9c65-42a2ace0bb30 · outbound

This paper cites Chebyshev polynomials.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks Chebyshev polynomials

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:09:10.991451Z

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Observation e9de0241-911c-44e7-9828-9d133b5c0688 · outbound

This paper cites The kolmogorov–arnold representation theorem revisited.

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks The kolmogorov–arnold representation theorem revisited

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:09:10.976233Z

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Pith citing papers

Observation b9ba1a6f-5ea5-4e43-9409-f614ec6457e0 · inbound

Augmented Physics-Based Li-ion Battery Model via Adaptive Ensemble Sparse Learning and Conformal Prediction cites this paper.

Augmented Physics-Based Li-ion Battery Model via Adaptive Ensemble Sparse Learning and Conformal Prediction Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks

Reference 31

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Observation a874a372-16b5-457c-bbd5-066ae660a3c4 · inbound

A Practitioner's Guide to Kolmogorov-Arnold Networks cites this paper.

A Practitioner's Guide to Kolmogorov-Arnold Networks Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks

Reference 66

Resolution: verified exact; arxiv_id, observed 2026-05-18T03:30:50.412154Z

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