KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics | Paper Citation Record

Observation a0718bc2-821e-42bb-a601-ed652b2861c5 · outbound

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

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning

Reference 1

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This paper cites Raissi, H.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Raissi, H

Reference 2

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This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 3

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This paper cites Raissi, A.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Raissi, A

Reference 4

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This paper cites Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks

Reference 7

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Reference 8

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Reference 9

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This paper cites Goodfellow, J.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Goodfellow, J

Reference 10

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This paper cites Vaswani, N.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Vaswani, N

Reference 11

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Reference 13

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Reference 14

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Reference 16

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This paper cites Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl

Reference 17

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Reference 20

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Reference 21

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Reference 22

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Observation 34c523bd-a0b7-49de-b3d5-ec3928b43dc1 · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics KAN: Kolmogorov-Arnold Networks

Reference 23

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

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics KAN 2.0: Kolmogorov-Arnold Networks Meet Science

Reference 24

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This paper cites On the expressiveness and spectral bias of KANs.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics On the expressiveness and spectral bias of KANs

Reference 25

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Reference 26

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This paper cites Smooth Kolmogorov Arnold networks enabling structural knowledge representation.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Smooth Kolmogorov Arnold networks enabling structural knowledge representation

Reference 27

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This paper cites Schmidhuber, Discovering neural nets with low Kolmogorov complexity and high generalization capability, Neural Networks 10 (5) (1997) 857–873.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Schmidhuber, Discovering neural nets with low Kolmogorov complexity and high generalization capability, Neural Networks 10 (5) (1997) 857–873

Reference 30

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Reference 31

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Reference 32

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This paper cites On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem

Reference 33

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics A Survey on Kolmogorov-Arnold Network

Reference 34

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Kolmogorov-Arnold Networks are Radial Basis Function Networks

Reference 36

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Wav-KAN: Wavelet Kolmogorov-Arnold Networks

Reference 37

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

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

Reference 39

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Shukla, J

Reference 41

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This paper cites DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems

Reference 43

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Zhang, T

Reference 44

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks

Reference 45

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Multifidelity Kolmogorov-Arnold Networks

Reference 46

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This paper cites Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations

Reference 49

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

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials

Reference 50

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Rigas, M

Reference 51

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Deep Learning Alternatives of the Kolmogorov Superposition Theorem

Reference 52

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks

Reference 53

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Igelnik, N

Reference 54

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This paper cites K ˙ urkov´ a, Kolmogorov’s theorem is relevant, Neural Computation 3 (4) (1991) 617–622.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics K ˙ urkov´ a, Kolmogorov’s theorem is relevant, Neural Computation 3 (4) (1991) 617–622

Reference 55

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This paper cites K ˙ urkov´ a, Kolmogorov’s theorem and multilayer neural networks, Neural net- works 5 (3) (1992) 501–506.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics K ˙ urkov´ a, Kolmogorov’s theorem and multilayer neural networks, Neural net- works 5 (3) (1992) 501–506

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Salimans, D

Reference 57

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

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics The information bottleneck method

Reference 60

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Dherin, M

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Learning in PINNs: Phase transition, total diffusion, and generalization

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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Observation 27b006c3-ea8d-473d-b747-29ced1a35f77 · outbound

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks

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Observation 139e7890-bd04-4750-89da-d340ac9fc5a1 · outbound

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Observation 0ff0d4e1-5a46-41e5-9715-fbc0fafe5014 · outbound

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Kolmogorov, On the representation of continuous functions of several variables as superpositions of continuous functions of one variable and additionEnglish translation: Amer

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Observation 313e7ee0-8ea5-4fd4-9840-958d510038c9 · outbound

This paper cites Girosi, T.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Girosi, T

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Observation b83e1989-088c-4f8c-802f-ebfa6b1e8558 · outbound

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Sprecher, Ph.d

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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Observation 069b4f82-134a-41ed-9ed1-c85569a2f781 · outbound

This paper cites Montanelli, H.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Montanelli, H

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This paper cites Braun, An Application of Kolmogorov’s Superposition Theorem to Function Reconstruction in Higher Dimensions, Ph.D.

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Observation 57a7d16f-4a0a-415f-b880-f2db6da002e9 · outbound

This paper cites Braun, M.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Braun, M

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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This paper cites Schmidt-Hieber, The Kolmogorov–Arnold representation theorem revisited, Neural Networks 137 (2021) 119–126.

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Observation ba46f429-251c-4b97-aa96-0fe18c4c0d01 · outbound

This paper cites Bader, Space-Filling Curves: An Introduction with Applications in Scientific Computing, Springer, Berlin, Heidelberg, 2013.

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Observation 3796826f-6caa-4b0d-b40e-2cbef5a49f92 · outbound

This paper cites Ismayilova, V.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Ismayilova, V

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Observation 6772d6e0-b9f9-4c7d-bd1a-b87b06ec174d · outbound

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Observation 1ec90f9b-647b-464a-8d07-83ae738a2a2f · outbound

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Observation 0ef3e011-d4ce-47c2-bc18-a0da8b882a5d · outbound

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Observation 97a734a1-1145-433d-a105-edc32f32ff22 · outbound

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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This paper cites Sternfeld, Dimension, superposition of functions and separation of points, in compact metric spaces, Israel Journal of Mathematics 50 (1985) 13–53.

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Observation bff62376-4efd-4565-8283-2523a00fd1b4 · outbound

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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Observation e77ef3e8-9be1-437c-8544-f23ee821f142 · outbound

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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Unresolved cited work

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Observation 0d93f6a9-4ed5-4366-bffe-eda3e952fb61 · outbound

This paper cites The Proof of Kolmogorov-Arnold May Illuminate Neural Network Learning.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics The Proof of Kolmogorov-Arnold May Illuminate Neural Network Learning

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Observation a0df066f-825d-4c85-aae9-a418b97bfad2 · outbound

This paper cites Petersen, J.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics Petersen, J

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Observation 11b54882-fd66-46dc-b501-d7e8fd74622a · outbound

This paper cites The Optimal Linear B-splines Approximation via Kolmogorov Superposition Theorem and its Application.

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics The Optimal Linear B-splines Approximation via Kolmogorov Superposition Theorem and its Application

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Observation 74710e33-754c-4e0c-b03e-86f457aaa8f1 · outbound

This paper cites Tensor Neural Network and Its Numerical Integration.

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