Paper Citation Record · LEDGER

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs

As of 10 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2606.29343.

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2606.29343 v1

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measured 41 of 41 reference resolution

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41 of 41 outbound references displayed

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Outbound references

Observation 8b11dee4-b278-4553-a0fb-f547928a31c3 · outbound

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

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Neural ordinary differential equations.Advances in neural information process- ing systems, 31, 2018

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 6ca9ed79-21c4-4c55-aa16-c136c0c3b14c · outbound

This paper cites A proposal on machine learning via dynamical systems.Links, 2024:08–27, 2017.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs A proposal on machine learning via dynamical systems.Links, 2024:08–27, 2017

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 4a0020c6-10e6-4d73-b677-876826cae94a · outbound

This paper cites Deep learning: An introduction for applied mathematicians.Siam review, 61(4):860–891, 2019.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Deep learning: An introduction for applied mathematicians.Siam review, 61(4):860–891, 2019

Reference 3

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Observation 681e06e5-9a85-4121-bc92-03845a723ea6 · outbound

This paper cites Cambridge University Press, 2022.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Cambridge University Press, 2022

Reference 4

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Observation a855232d-a27c-4c38-b47c-63b4b4a9212a · outbound

This paper cites Neural ode control for classification, approximation, and transport.SIAM Review, 65(3):735–773, 2023.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Neural ode control for classification, approximation, and transport.SIAM Review, 65(3):735–773, 2023

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 2e3ccb5e-afd6-4abb-8062-c4fc760aac0d · outbound

This paper cites Universal Approximation Property of Neural Ordinary Differential Equations.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Universal Approximation Property of Neural Ordinary Differential Equations

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T02:44:11.459218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 205e7914-31da-42f7-b1b0-f714f98048ec · outbound

This paper cites Universal approxi- mation of dynamical systems by semiautonomous neural odes and applications.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Universal approxi- mation of dynamical systems by semiautonomous neural odes and applications

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 98a32ad3-40bc-4077-b14e-819fe301a1fc · outbound

This paper cites Interpolation and ap- proximation via momentum resnets and neural odes.Systems & Control Letters, 162:105182, 2022.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Interpolation and ap- proximation via momentum resnets and neural odes.Systems & Control Letters, 162:105182, 2022

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation eb1f6c59-a2e6-42ee-afd8-5ce483227326 · outbound

This paper cites Interpolation, approx- imation, and controllability of deep neural networks.SIAM Journal on Control and Optimization, 63(1):625–649, 2025.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Interpolation, approx- imation, and controllability of deep neural networks.SIAM Journal on Control and Optimization, 63(1):625–649, 2025

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation c7eb81d1-976e-4d5c-bf2f-dc16d5cc2d87 · outbound

This paper cites Interplay between depth and width for interpolation in neural odes.Neural Networks, 180:106640, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Interplay between depth and width for interpolation in neural odes.Neural Networks, 180:106640, 2024

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation c9b21c17-8287-4ca3-8936-1a3615f6d331 · outbound

This paper cites Generalization bounds for neural ordinary differential equations and deep residual networks.Advances in neural information processing systems, 36:48918–48938, 2023.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Generalization bounds for neural ordinary differential equations and deep residual networks.Advances in neural information processing systems, 36:48918–48938, 2023

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 94493247-cb7f-4f29-bcbf-9e1b18ccbef0 · outbound

This paper cites Deep neural networks, generic universal interpolation, and controlled odes.SIAM Journal on Mathe- matics of Data Science, 2(3):901–919, 2020.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Deep neural networks, generic universal interpolation, and controlled odes.SIAM Journal on Mathe- matics of Data Science, 2(3):901–919, 2020

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation f0875eea-fe18-4d87-80e5-ae72bfcc8269 · outbound

This paper cites Neural ode control for trajectory approximation of continuity equation.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Neural ode control for trajectory approximation of continuity equation

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 92ec6507-9d23-419a-b38b-ecbf19f8965f · outbound

This paper cites Constructive interpolation and generalization rates for neural ODEs: a control perspective.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Constructive interpolation and generalization rates for neural ODEs: a control perspective

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-06-30T02:44:11.463015Z

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Observation 669079c8-1961-4162-950a-84766e38ae9a · outbound

This paper cites Learning on manifolds: Universal approximations properties using geometric 4 controllability conditions for neural odes.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Learning on manifolds: Universal approximations properties using geometric 4 controllability conditions for neural odes

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation a4ec58b9-d3e8-4ffe-ae36-d3eaf3b5b92b · outbound

This paper cites Sparsity in long-time control of neural odes.Systems & Control Letters, 172:105452, 2023.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Sparsity in long-time control of neural odes.Systems & Control Letters, 172:105452, 2023

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 169eb535-fb46-45c6-8a3f-de1093140f17 · outbound

This paper cites Turnpike in optimal control of pdes, resnets, and beyond.Acta Numerica, 31:135–263, 2022.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Turnpike in optimal control of pdes, resnets, and beyond.Acta Numerica, 31:135–263, 2022

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 3113653e-1abe-44b3-89d8-36358c6a23a5 · outbound

This paper cites Augmented neural odes.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Augmented neural odes

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 260754ad-08c9-409c-a013-041f21e7918e · outbound

This paper cites Neuralcontrolled differential equations for irregular time series.Advances in neural information processing systems, 33:6696–6707, 2020.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Neuralcontrolled differential equations for irregular time series.Advances in neural information processing systems, 33:6696–6707, 2020

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 72afc9e4-5b25-4d4a-a888-cfd137aa98c6 · outbound

This paper cites Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 41923100-a02f-4266-996d-d3b0d47bb51a · outbound

This paper cites Stable architectures for deep neural networks.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Stable architectures for deep neural networks

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 2fca194c-a9ff-4749-8dcc-adc020860837 · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation fcd6d283-91ee-4589-8a98-390b6768c364 · outbound

This paper cites Universal approximation bounds for superpositions of a sigmoidal function.IEEE Transactions on Information theory, 39(3):930–945, 2002.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Universal approximation bounds for superpositions of a sigmoidal function.IEEE Transactions on Information theory, 39(3):930–945, 2002

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 41de74f8-2a3a-4673-940a-6f928a6e1de2 · outbound

This paper cites Approximation theory of the mlp model in neural networks.Acta numerica, 8:143–195, 1999.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Approximation theory of the mlp model in neural networks.Acta numerica, 8:143–195, 1999

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 44b3ff84-5640-4505-8d26-df8c9936459b · outbound

This paper cites The barron space and the flow-induced function spaces for neural network models.Constructive Approximation, 55(1):369–406, 2022.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs The barron space and the flow-induced function spaces for neural network models.Constructive Approximation, 55(1):369–406, 2022

Reference 25

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Observation 2cf55497-ab68-4b63-b729-0f5be76ecce4 · outbound

This paper cites Solving high-dimensional partial differential equations using deep learning.Proceedings of the National Academy of Sciences, 115(34):8505–8510, 2018.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Solving high-dimensional partial differential equations using deep learning.Proceedings of the National Academy of Sciences, 115(34):8505–8510, 2018

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation ab95cdd9-d5f3-48ef-a118-2cdda6219d40 · outbound

This paper cites Optimal approximation of zonoids and uniform approxima- tion by shallow neural networks.Constructive Approximation, 62(2):441–469, 2025.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Optimal approximation of zonoids and uniform approxima- tion by shallow neural networks.Constructive Approximation, 62(2):441–469, 2025

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 82b8aeda-e091-452e-a733-294ebc242c81 · outbound

This paper cites Sharp bounds on the approximation rates, metric entropy, and n-widths of shallow neural networks.Foundations of Com- putational Mathematics, 24(2):481–537, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Sharp bounds on the approximation rates, metric entropy, and n-widths of shallow neural networks.Foundations of Com- putational Mathematics, 24(2):481–537, 2024

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation f486fad3-d291-4437-b942-f72e1147346a · outbound

This paper cites Two-layer networks with the relu k activation function: Barron spaces and derivative ap- proximation.Numerische Mathematik, 156(1):319–344, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Two-layer networks with the relu k activation function: Barron spaces and derivative ap- proximation.Numerische Mathematik, 156(1):319–344, 2024

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 1e061872-b34d-480b-b167-b4018ab13480 · outbound

This paper cites Spectral barron space for deep neural network approximation.SIAM Journal on Mathematics of Data Science, 7(3):1053–1076, 2025.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Spectral barron space for deep neural network approximation.SIAM Journal on Mathematics of Data Science, 7(3):1053–1076, 2025

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 16fbb7c6-9309-4760-985a-4ce83e52502c · outbound

This paper cites Neural operators for accelerating sci- entific simulations and design.Nature Reviews Physics, 6(5):320–328, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Neural operators for accelerating sci- entific simulations and design.Nature Reviews Physics, 6(5):320–328, 2024

Reference 31

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Observation d935b52e-e28e-4a70-bb61-b7eb1ef9c94e · outbound

This paper cites Laplace neural operator for solving differential equations.Nature Machine Intelligence, 6(6): 631–640, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Laplace neural operator for solving differential equations.Nature Machine Intelligence, 6(6): 631–640, 2024

Reference 32

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Observation f860d771-aa85-469b-ac8b-cd91633a58af · outbound

This paper cites Spectral op- erator learning for parametric pdes without data reliance.Computer Methods in Applied Mechanics and Engineering, 420:116678, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Spectral op- erator learning for parametric pdes without data reliance.Computer Methods in Applied Mechanics and Engineering, 420:116678, 2024

Reference 33

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Observation f8c8e844-6b8f-4ac8-9b80-a6b792a3f85f · outbound

This paper cites Neural operators for adaptive control of freeway traffic.Automatica, 182:112553, 2025.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Neural operators for adaptive control of freeway traffic.Automatica, 182:112553, 2025

Reference 34

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Observation 9b46836e-af85-425f-ac49-f2e3eb1e7fd3 · outbound

This paper cites Improved gener- alization with deep neural operators for engineering systems: Path towards dig- ital twin.Engineering Applications of Artificial Intelligence, 131:107844, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Improved gener- alization with deep neural operators for engineering systems: Path towards dig- ital twin.Engineering Applications of Artificial Intelligence, 131:107844, 2024

Reference 35

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Observation 1cc86955-914b-4a42-add6-1eb77f4e2304 · outbound

This paper cites Deep neural operator-driven real-time inference to enable digital twin solutions for nuclear energy systems.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Deep neural operator-driven real-time inference to enable digital twin solutions for nuclear energy systems

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 827964f8-97f0-450c-839c-5903c002c679 · outbound

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Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation f48cc541-dd4e-4371-959c-4e77d9e8db4e · outbound

This paper cites The admm-pinns algorith- mic framework for nonsmooth pde-constrained optimization: a deep learning approach.SIAM Journal on Scientific Computing, 46(6):C659–C687, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs The admm-pinns algorith- mic framework for nonsmooth pde-constrained optimization: a deep learning approach.SIAM Journal on Scientific Computing, 46(6):C659–C687, 2024

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 444d2893-b65e-4eb7-b887-540121490a84 · outbound

This paper cites The hard-constraint pinns for interface optimal control problems.SIAM Journal on Scientific Computing, 47(3):C601–C629, 2025.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs The hard-constraint pinns for interface optimal control problems.SIAM Journal on Scientific Computing, 47(3):C601–C629, 2025

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 004d28c1-a896-43a8-947d-620704771077 · outbound

This paper cites Respecting causality for training physics-informed neural networks.Computer Methods in Applied Me- chanics and Engineering, 421:116813, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Respecting causality for training physics-informed neural networks.Computer Methods in Applied Me- chanics and Engineering, 421:116813, 2024

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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Observation 302fdc50-653d-4811-a18b-7d8296b1ec1f · outbound

This paper cites Control of neural transport for nor- malising flows.Journal de Mathématiques Pures et Appliquées, 181:58–90, 2024.

Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs Control of neural transport for nor- malising flows.Journal de Mathématiques Pures et Appliquées, 181:58–90, 2024

Reference 41

Resolution: unresolved; no resolver link, observed 2026-06-30T02:42:00.982282Z

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