Paper Citation Record · LEDGER

Space-time error estimates for deep neural network approximations for differential equations

As of 15 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 2 inbound Pith citation observations for arXiv:1908.03833.

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

pith.paper-citation-record.v1
1908.03833 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:10:00.029939Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T10:39:29.571077Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-24T12:39:29.035712Z

Reference resolution

37 of 37 outbound references displayed

verified exact5
verified fuzzy2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4d2e7726-f2c8-4bd4-b380-96d12127716b · outbound

This paper cites Deep splitting method for parabolic PDEs.

Space-time error estimates for deep neural network approximations for differential equations Deep splitting method for parabolic PDEs

Reference 1

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Observation aa5397f1-36ce-4dd3-a889-85795953e213 · outbound

This paper cites Solving the Kolmogorov PDE by means of deep learning.

Space-time error estimates for deep neural network approximations for differential equations Solving the Kolmogorov PDE by means of deep learning

Reference 2

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Observation fde555e0-4a45-4553-84fe-2b7c5e4989cc · outbound

This paper cites Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Diﬀerential Eq ua- tions and Second-order Backward Stochastic Diﬀerential Equatio ns.

Space-time error estimates for deep neural network approximations for differential equations Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Diﬀerential Eq ua- tions and Second-order Backward Stochastic Diﬀerential Equatio ns

Reference 3

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Observation 0b590230-77e0-4372-a048-47ec34ebe864 · outbound

This paper cites Deep Optimal Stopping.

Space-time error estimates for deep neural network approximations for differential equations Deep Optimal Stopping

Reference 4

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Observation e6b167d0-910c-4a88-92a0-56f2c274d66a · outbound

This paper cites Solving high-dimensional optimal stopping problems using deep learning.

Space-time error estimates for deep neural network approximations for differential equations Solving high-dimensional optimal stopping problems using deep learning

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T14:09:59.848604Z

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Observation 12f664d7-5278-40e0-8888-ff3b5a114dcc · outbound

This paper cites A uniﬁed deep artiﬁcial neural network ap- proach to partial diﬀerential equations in complex geometries.

Space-time error estimates for deep neural network approximations for differential equations A uniﬁed deep artiﬁcial neural network ap- proach to partial diﬀerential equations in complex geometries

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T14:09:59.853975Z

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Observation 7e3a4ad6-049e-4597-a8f6-77d7bb36312c · outbound

This paper cites Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations.

Space-time error estimates for deep neural network approximations for differential equations Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-14T14:09:59.860563Z

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Observation 9f4e3622-17d3-4b1e-8953-7950a8d5ff0b · outbound

This paper cites Machine Learning for Semi Linear PDEs.

Space-time error estimates for deep neural network approximations for differential equations Machine Learning for Semi Linear PDEs

Reference 8

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Observation b7695792-b12d-44f7-a586-7d222c0ffaaa · outbound

This paper cites Deep Learning-Based Numerical Meth- ods for High-Dimensional Parabolic Partial Diﬀerential Equations an d Back- ward Stochastic Diﬀerential Equations.

Space-time error estimates for deep neural network approximations for differential equations Deep Learning-Based Numerical Meth- ods for High-Dimensional Parabolic Partial Diﬀerential Equations an d Back- ward Stochastic Diﬀerential Equations

Reference 9

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Observation fd70ed99-5f3c-4518-9af5-e7b6c3b8a1b1 · outbound

This paper cites The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems.

Space-time error estimates for deep neural network approximations for differential equations The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

Reference 10

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Observation beeafcd8-48f3-41b3-805c-5b7083ac30d2 · outbound

This paper cites DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing.

Space-time error estimates for deep neural network approximations for differential equations DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing

Reference 11

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Observation cb99c212-3e76-4980-a154-a408b8b289ad · outbound

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Space-time error estimates for deep neural network approximations for differential equations Unresolved cited work

Reference 12

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Observation 25165fdd-16d1-48c7-81b5-ecf775ddecf7 · outbound

This paper cites Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDE s.

Space-time error estimates for deep neural network approximations for differential equations Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDE s

Reference 13

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Observation f7204106-cc32-491d-82ad-25e3ed531493 · outbound

This paper cites Deep Learning.

Space-time error estimates for deep neural network approximations for differential equations Deep Learning

Reference 14

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Observation 22cf2e73-b51e-410a-b343-41ff2b915788 · outbound

This paper cites Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension.

Space-time error estimates for deep neural network approximations for differential equations Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension

Reference 15

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Observation a271a83e-d74a-468d-9aa4-a1c388a39348 · outbound

This paper cites A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.

Space-time error estimates for deep neural network approximations for differential equations A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

Reference 16

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Observation b16a480f-bc18-4651-b627-d42ba730c92b · outbound

This paper cites Deep Neural Network Approximation Theory.

Space-time error estimates for deep neural network approximations for differential equations Deep Neural Network Approximation Theory

Reference 17

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Observation 31c60b9c-1ad4-450f-805b-824e218738aa · outbound

This paper cites Solving high-dimensional partial diﬀer- ential equations using deep learning.

Space-time error estimates for deep neural network approximations for differential equations Solving high-dimensional partial diﬀer- ential equations using deep learning

Reference 18

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Observation d578caad-4fb0-43ad-93fc-625d9e727f51 · outbound

This paper cites Convergence of the Deep BSDE Method for Coupled FBSDEs.

Space-time error estimates for deep neural network approximations for differential equations Convergence of the Deep BSDE Method for Coupled FBSDEs

Reference 19

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Observation 4482d8b5-fa44-4cca-a737-6b0c052d0c9b · outbound

This paper cites Deep Primal-Dual Algorithm for BSDEs: Appli- cations of Machine Learning to CV A and IM.

Space-time error estimates for deep neural network approximations for differential equations Deep Primal-Dual Algorithm for BSDEs: Appli- cations of Machine Learning to CV A and IM

Reference 20

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Observation 4e5d8bcd-2501-4d33-b081-4e1270b7e67c · outbound

This paper cites Some machine learning schemes for high-dimensional nonlinear PDEs.

Space-time error estimates for deep neural network approximations for differential equations Some machine learning schemes for high-dimensional nonlinear PDEs

Reference 21

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Observation 1ebe2c1d-4547-40e5-999f-9801a039a1ac · outbound

This paper cites A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations.

Space-time error estimates for deep neural network approximations for differential equations A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-14T14:09:59.942163Z

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Observation 0397eebb-1a8a-4abe-8ed3-8c1ce9e2ec56 · outbound

This paper cites Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks.

Space-time error estimates for deep neural network approximations for differential equations Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks

Reference 23

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Observation 86ef2b73-57f4-409a-8b7d-1773c3df2f8e · outbound

This paper cites Deep Curve-dependent PDEs for affine rough volatility.

Space-time error estimates for deep neural network approximations for differential equations Deep Curve-dependent PDEs for affine rough volatility

Reference 24

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Observation 32bf5e20-1e7c-42cd-9e2e-784c96337a12 · outbound

This paper cites A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients.

Space-time error estimates for deep neural network approximations for differential equations A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

Reference 25

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Observation 6700ef96-9487-4d65-a60c-c777af57e341 · outbound

This paper cites A Theoretical Analysis of Deep Neural Networks and Parametric PDEs.

Space-time error estimates for deep neural network approximations for differential equations A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

Reference 26

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Observation 4669c1f1-3330-49d9-90c2-4fc8cc3b38f3 · outbound

This paper cites Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units.

Space-time error estimates for deep neural network approximations for differential equations Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-14T14:09:59.969053Z

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Observation 95c60763-9630-49a5-a9e9-38de4e7fe3ce · outbound

This paper cites PDE-Net: Learning PDEs from Data.

Space-time error estimates for deep neural network approximations for differential equations PDE-Net: Learning PDEs from Data

Reference 28

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Observation 2c192648-04f5-49c6-bb1d-1cb2296b23de · outbound

This paper cites Deep learning observables in computational fluid dynamics.

Space-time error estimates for deep neural network approximations for differential equations Deep learning observables in computational fluid dynamics

Reference 29

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Observation 1bd0c10a-66f5-4341-ae21-9ba4f343654d · outbound

This paper cites Neural Networks Trained to Solve Diﬀerential Equations Learn General Representations.

Space-time error estimates for deep neural network approximations for differential equations Neural Networks Trained to Solve Diﬀerential Equations Learn General Representations

Reference 30

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Observation b27f6a0f-bf3a-4d6d-8b56-a1f1540142f7 · outbound

This paper cites Topological properties of the set of functions generated by neural networks of fixed size.

Space-time error estimates for deep neural network approximations for differential equations Topological properties of the set of functions generated by neural networks of fixed size

Reference 31

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Observation 02a6a453-3f17-4410-8907-6b57f631684c · outbound

This paper cites Optimal approximation of piecewise smooth functions using deep ReLU neural networks.

Space-time error estimates for deep neural network approximations for differential equations Optimal approximation of piecewise smooth functions using deep ReLU neural networks

Reference 32

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Observation a7b0f207-d5c7-49f7-bfab-6c4993bab670 · outbound

This paper cites Neural networks-based backward scheme for fully nonlinear PDEs.

Space-time error estimates for deep neural network approximations for differential equations Neural networks-based backward scheme for fully nonlinear PDEs

Reference 33

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Observation defd40a7-bd4d-4338-afef-65c171a3af1e · outbound

This paper cites Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations.

Space-time error estimates for deep neural network approximations for differential equations Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

Reference 34

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Observation 64c46afe-3e9c-44ac-8824-ea715c91c775 · outbound

This paper cites Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems.

Space-time error estimates for deep neural network approximations for differential equations Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems

Reference 35

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Observation 86ea9583-7005-47f9-bdf8-9bd9082bf7e5 · outbound

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

Space-time error estimates for deep neural network approximations for differential equations DGM: A deep learning algorithm for solving partial diﬀerential equations

Reference 36

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Source-reported events for the cited work

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Observation 0e7c5bfd-1a0b-4d02-b608-a57217f26a22 · outbound

This paper cites Error bounds for approximations with deep ReLU networks.

Space-time error estimates for deep neural network approximations for differential equations Error bounds for approximations with deep ReLU networks

Reference 37

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Pith citing papers

Observation 21c3664a-7cdf-4956-bdf0-bc9fe3e66a91 · inbound

Deep neural network approximations for Monte Carlo algorithms cites this paper.

Deep neural network approximations for Monte Carlo algorithms Space-time error estimates for deep neural network approximations for differential equations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:29.571077Z

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Observation e0a8488b-f832-452c-87c2-8b86076f848d · inbound

Deep neural network approximation theory for high-dimensional functions cites this paper.

Deep neural network approximation theory for high-dimensional functions Space-time error estimates for deep neural network approximations for differential equations

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-24T12:39:29.039070Z

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