Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks | Paper Citation Record

Observation 4f648a47-4e55-41df-9e54-f4414b776c82 · outbound

This paper cites Solution of a partial integro-differential equation arising from viscoelasticity.Interna- tional Journal of Computer Mathematics, 83(1):123–129, 2006.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Solution of a partial integro-differential equation arising from viscoelasticity.Interna- tional Journal of Computer Mathematics, 83(1):123–129, 2006

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This paper cites Asymptotic stability in viscoelasticity.Archive for rational mechanics and analysis, 37(4):297–308, 1970.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Asymptotic stability in viscoelasticity.Archive for rational mechanics and analysis, 37(4):297–308, 1970

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This paper cites Diffusion with memory in two cases of biological interest.Journal of theoretical biology, 254(3):697–703, 2008.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Diffusion with memory in two cases of biological interest.Journal of theoretical biology, 254(3):697–703, 2008

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This paper cites The random walk’s guide to anomalous diffusion: a fractional dynamics approach.Physics reports, 339(1):1–77, 2000.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks The random walk’s guide to anomalous diffusion: a fractional dynamics approach.Physics reports, 339(1):1–77, 2000

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This paper cites Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

Reference 5

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This paper cites A general theory of heat conduction with finite wave speeds.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks A general theory of heat conduction with finite wave speeds

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This paper cites On heat conduction in materials with memory.Quarterly of Applied Mathematics, 29 (2):187–204, 1971.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks On heat conduction in materials with memory.Quarterly of Applied Mathematics, 29 (2):187–204, 1971

Reference 7

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This paper cites Fast and oblivious convolution quadrature.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Fast and oblivious convolution quadrature

Reference 8

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This paper cites A kernel-independent sum-of-exponentials method.Journal of Scientific Computing, 93(2):40, 2022.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks A kernel-independent sum-of-exponentials method.Journal of Scientific Computing, 93(2):40, 2022

Reference 9

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This paper cites Optimal prediction and the mori–zwanzig rep- resentation of irreversible processes.Proceedings of the National Academy of Sciences, 97(7):2968–2973, 2000.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Optimal prediction and the mori–zwanzig rep- resentation of irreversible processes.Proceedings of the National Academy of Sciences, 97(7):2968–2973, 2000

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This paper cites A priori estimation of memory effects in reduced- ordermodelsofnonlinearsystemsusingthemori–zwanzigformalism.Proceedings.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks A priori estimation of memory effects in reduced- ordermodelsofnonlinearsystemsusingthemori–zwanzigformalism.Proceedings

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This paper cites Identification of a relaxation kernel using two boundary measures.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Identification of a relaxation kernel using two boundary measures

Reference 12

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This paper cites Memory kernel reconstruction problems in the integro-differential equation of rigid heat conductor.Mathematical Methods in the Applied Sciences, 45 (14):8374–8388, 2022.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Memory kernel reconstruction problems in the integro-differential equation of rigid heat conductor.Mathematical Methods in the Applied Sciences, 45 (14):8374–8388, 2022

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This paper cites Kernel determination problem for a integro–differential heat equation with a variable thermal conductivity.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Kernel determination problem for a integro–differential heat equation with a variable thermal conductivity

Reference 14

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This paper cites Inverse problems for memory kernels by laplace transform methods.Zeitschrift für Analysis und ihre Anwendungen, 19(2):489–510, 2000.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Inverse problems for memory kernels by laplace transform methods.Zeitschrift für Analysis und ihre Anwendungen, 19(2):489–510, 2000

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Observation 41beb2e4-460a-47ac-9da4-fc44b53318c1 · outbound

This paper cites Identifying memory kernels in linear thermoviscoelasticity of boltzmann type.Mathematical Models and Methods in Applied Sciences, 4(06):807–842, 1994.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Identifying memory kernels in linear thermoviscoelasticity of boltzmann type.Mathematical Models and Methods in Applied Sciences, 4(06):807–842, 1994

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This paper cites A survey of regularization methods for first-kind volterra equations.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks A survey of regularization methods for first-kind volterra equations

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This paper cites Identification of the relaxation kernel in diffusion processes and viscoelasticity with memory via deconvolution.Mathematical Methods in the Applied Sciences, 40(7):2542–2549, 2017.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Identification of the relaxation kernel in diffusion processes and viscoelasticity with memory via deconvolution.Mathematical Methods in the Applied Sciences, 40(7):2542–2549, 2017

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This paper cites Application of prony series to linear viscoelasticity.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Application of prony series to linear viscoelasticity

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This paper cites Brunton, Joshua L.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Brunton, Joshua L

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This paper cites Neural ordinary differential equations.Advances in neural information processing systems, 31, 2018.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Neural ordinary differential equations.Advances in neural information processing systems, 31, 2018

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This paper cites Rudy, Steven L.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Rudy, Steven L

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This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, 2021.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, 2021

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Symbolic–kan: Kolmogorov-arnold networks with discrete symbolic structure for interpretable learning.arXiv preprint arXiv:2603.23854, 2026

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Unresolved cited work

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This paper cites Minpo: Memory-informed neural pseudo- operator to resolve nonlocal spatiotemporal dynamics.arXiv preprint arXiv:2512.17273, 2025.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Minpo: Memory-informed neural pseudo- operator to resolve nonlocal spatiotemporal dynamics.arXiv preprint arXiv:2512.17273, 2025

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Physics informed neural networks for an inverse problem in peridynamic models.Engineering with Computers, 41(6):4003–4012, 2025

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Learning memory kernels in second-order volterra models: a data-driven approach for viscoelastic systems.Mechanics of Time-Dependent Materials, 30(2): 42, 2026

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Sparse identification of delay equations with distributed memory.arXiv preprint arXiv:2512.21070, 2025

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Unresolved cited work

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Physics-guided symbolic regression of nonlocal transport memory from sparse observations in aquatic systems.Preprint, available at SSRN 6404003, 2026

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Neural integro-differential equations

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Learning integral operators via neural integral equations.Nature Machine Intelligence, 6(9):1046–1062, 2024

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks ANODE: Unconditionally accurate memory-efficient gra- dients for neural ODEs

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Discretize-Optimize vs. Optimize-Discretize for Time-Series Regression and Continuous Normalizing Flows

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks A simple proof of a duality theorem with applications in scalar and anisotropic viscoelasticity

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks On complete monotonicity of solution to the fractional relaxation equation with the n th level fractional derivative.Mathematics, 8(9):1561, 2020

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Wave propagation in linear viscoelastic media with completely monotonic relaxation moduli.Wave Motion, 50(5):909–928, 2013

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Kolmogorov- arnold networks for data-driven, physics-informed, and deep-operator learning: a review, synthesis, and new analysis.Neural networks, page 108791, 2026

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Scaled-cpikans: Spatial variable and residual scaling in chebyshev-based physics-informed kolmogorov-arnold networks.Journal of Computational Physics, 537: 114116, 2025

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks KAN or MLP: A Fairer Comparison

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Input convex neural networks

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Observation 78975135-6d50-4a04-9fd9-6eb7e8b008d1 · outbound

This paper cites Monotonic networks.Advances in neural information processing systems, 10, 1997.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Monotonic networks.Advances in neural information processing systems, 10, 1997

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Observation 242271f7-3164-42dc-aaad-c57391af6524 · outbound

This paper cites an unresolved cited work.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Unresolved cited work

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Observation 25f4f6d4-5693-46fe-9a1c-85b952d17eb8 · outbound

This paper cites an unresolved cited work.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Unresolved cited work

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Observation 578ab9d2-32d3-4efc-935f-9d493eba08b7 · outbound

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Input convex kolmogorov arnold networks.arXiv preprint arXiv:2505.21208, 2026

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Observation 7a8d0518-b03d-4b4a-b084-6c5f67ba17c9 · outbound

This paper cites The bernstein polynomial basis: A centennial retrospective.Computer Aided Geometric Design, 29(6):379–419, 2012.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks The bernstein polynomial basis: A centennial retrospective.Computer Aided Geometric Design, 29(6):379–419, 2012

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Observation 629be40b-16ab-4537-9049-93e4c8d1b750 · outbound

This paper cites Kan: Kolmogorov–arnold networks.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Kan: Kolmogorov–arnold networks

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

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials

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Observation 47623d8f-99e0-4b3e-bc14-dc07bfa02b8b · outbound

This paper cites Physics-informed kolmogorov– arnold network with chebyshev polynomials for fluid mechanics.Physics of Fluids, 37(9), 2025.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Physics-informed kolmogorov– arnold network with chebyshev polynomials for fluid mechanics.Physics of Fluids, 37(9), 2025

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Observation 26fb43d8-5fca-499a-8a84-b188ed11e9e9 · outbound

This paper cites Auto- matic differentiation in machine learning: a survey.Journal of machine learning research, 18(153):1–43, 2018.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Auto- matic differentiation in machine learning: a survey.Journal of machine learning research, 18(153):1–43, 2018

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Observation da8d96c3-e8bd-4a58-8627-8002891c8a06 · outbound

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Pytorch: An imperative style, high- performance deep learning library.Advances in neural information processing systems, 32, 2019

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Observation 3e234e40-0489-4460-99ed-33ab973fc9de · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Adam: A Method for Stochastic Optimization

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Observation 1c747b3e-1fdf-47b3-8d68-da59ffdffa88 · outbound

This paper cites On the limited memory bfgs method for large scale optimization.Math- ematical programming, 45(1):503–528, 1989.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks On the limited memory bfgs method for large scale optimization.Math- ematical programming, 45(1):503–528, 1989

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Observation 25bd8bed-29b2-406b-8549-709d6efe1c83 · outbound

This paper cites Line search algorithms with guaranteed sufficient decrease.ACM Transactions on Mathematical Software (TOMS), 20(3):286–307, 1994.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Line search algorithms with guaranteed sufficient decrease.ACM Transactions on Mathematical Software (TOMS), 20(3):286–307, 1994

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Observation 6eff7f5c-c2af-4138-a4bc-2c3f885d175d · outbound

This paper cites Cambridge University Press, 2017.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Cambridge University Press, 2017

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This paper cites Springer Science & Business Media, 2013.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Springer Science & Business Media, 2013

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Observation bf29d089-9588-4a2d-8adb-209e18c5def6 · outbound

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Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks World Scientific, 2022

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Observation 95db934f-98af-4e74-b5de-543cf04cd6f8 · outbound

This paper cites Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function.Transactions of the Faraday society, 66:80–85, 1970.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function.Transactions of the Faraday society, 66:80–85, 1970

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Observation b9befde9-ed86-4095-8087-c704b633b729 · outbound

This paper cites Detailed comparison of the williams–watts and cole– davidson functions.The Journal of chemical physics, 73(7):3348–3357, 1980.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Detailed comparison of the williams–watts and cole– davidson functions.The Journal of chemical physics, 73(7):3348–3357, 1980

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Observation 21d49321-3061-4195-87a2-b95201b176d7 · outbound

This paper cites Traveling waves in a convolution model for phase transitions.Archive for Rational Mechanics and Analysis, 138(2):105–136, 1997.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Traveling waves in a convolution model for phase transitions.Archive for Rational Mechanics and Analysis, 138(2):105–136, 1997

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Observation 532ae18c-fd87-491a-9656-5731a8e3ecaf · outbound

This paper cites Numerical analysis for a nonlocal allen-cahn equation.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Numerical analysis for a nonlocal allen-cahn equation

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Observation fa1e7aa1-1838-405e-959a-40edd8b08622 · outbound

This paper cites A nonlocal continuum model for biological aggregation.Bulletin of mathematical biology, 68(7):1601–1623, 2006.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks A nonlocal continuum model for biological aggregation.Bulletin of mathematical biology, 68(7):1601–1623, 2006

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Observation da34c62d-8aa0-4b3f-a176-ea54111cf7b6 · outbound

This paper cites Swarm dynamics and equilibria for a nonlocal aggregation model.Nonlinearity, 24(10):2681–2716, 2011.

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks Swarm dynamics and equilibria for a nonlocal aggregation model.Nonlinearity, 24(10):2681–2716, 2011

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