Paper Citation Record · LEDGER

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data

As of 16 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:1908.03190.

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

pith.paper-citation-record.v1
1908.03190 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:26:32.872990Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

41 of 41 outbound references displayed

verified exact0
verified fuzzy26
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cef7012a-1dfe-4e8a-8df5-02aac48c0c1a · outbound

This paper cites https://github.com/zalandoresearch/fashion-mnist.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data https://github.com/zalandoresearch/fashion-mnist

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.548088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4e7d78bc-120d-45a1-b9b0-928e6a5fd76a · outbound

This paper cites https://github.com/kefth/fashion-mnist.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data https://github.com/kefth/fashion-mnist

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.530153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 55b58ca0-ffb8-4f18-9f71-e6ffaa9dd5eb · outbound

This paper cites https://github.com/heitorrapela/fashion-mnist-mlp.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data https://github.com/heitorrapela/fashion-mnist-mlp

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.513818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 82ba9942-9770-47a8-95b0-f74dcde9e29d · outbound

This paper cites Discovering governing equations from data by sparse identiﬁcation of nonlinear dynamical systems.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Discovering governing equations from data by sparse identiﬁcation of nonlinear dynamical systems

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.497632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c755bf86-4304-4a3d-a131-42e5b8ef6565 · outbound

This paper cites Neural ordinary diﬀerential equations.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Neural ordinary diﬀerential equations

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.481566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 415ab60e-19fc-4b46-837a-cad367cb0e05 · outbound

This paper cites Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.699256Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d76fde5-67e9-4287-9e34-a12845507590 · outbound

This paper cites A proposal on machine learning via dynamical systems.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data A proposal on machine learning via dynamical systems

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.465452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 53c212cd-de9c-4ac2-bdd9-8176edd48bcc · outbound

This paper cites ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.709432Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b665e70f-9657-41a7-ad9d-2e8cc89b111b · outbound

This paper cites Learning, invariance, and generalization in high-order neural networks.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Learning, invariance, and generalization in high-order neural networks

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.714732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14ecacf8-d213-4668-b4c1-423ba5a554ee · outbound

This paper cites Stable architectures for deep neural networks.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Stable architectures for deep neural networks

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.437225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ee17c438-544c-4d6a-a558-1f9b2e072236 · outbound

This paper cites Deep residual learning for image recognition.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Deep residual learning for image recognition

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.419299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation caea54f5-7906-465e-95a6-eb2bd1d51ba3 · outbound

This paper cites Identity mappings in deep residual networks.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Identity mappings in deep residual networks

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.403291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 68f30157-62d9-44e3-b9b3-66bb0d71d63f · outbound

This paper cites Turbulence, coherent structures, dynamical systems and symmetry.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Turbulence, coherent structures, dynamical systems and symmetry

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.386234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1fee7ccc-288a-4d01-87ac-16e7b19c6fe1 · outbound

This paper cites Weinberger.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Weinberger

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.369493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7786c670-e5d9-4963-bfbf-5958aabe2680 · outbound

This paper cites Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.744375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1296fa4-29bd-412a-a532-8243212ed794 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Adam: A Method for Stochastic Optimization

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.749855Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6040b968-8d72-49d5-8941-5662272b5894 · outbound

This paper cites Nathan Kutz, Steven L.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Nathan Kutz, Steven L

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.353461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6826c95b-22e1-40b6-987f-5b02f07796d0 · outbound

This paper cites Dynamic mode decomposition: data-driven modeling of complex systems.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Dynamic mode decomposition: data-driven modeling of complex systems

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.759995Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ec7f24c-c4a1-44a7-948d-bcfa07527ae6 · outbound

This paper cites FractalNet: Ultra-deep neural networks without residuals.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data FractalNet: Ultra-deep neural networks without residuals

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.325538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 532dd5b3-3891-4e32-bac5-d318aceaca90 · outbound

This paper cites Gradient-based learning applied to document recognition.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Gradient-based learning applied to document recognition

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.309918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 162514a6-f9e3-46be-b697-84a38656dbe5 · outbound

This paper cites PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.774055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f3a7b7d-414e-429f-8c2d-d3963a5f1c43 · outbound

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

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data PDE-Net: Learning PDEs from Data

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.779680Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80bf7ea9-670e-4415-b37b-8d0bd154380c · outbound

This paper cites Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.784577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58a23d84-f90e-47bb-ba16-bc6fe046a105 · outbound

This paper cites Autograd: Reverse-mode diﬀeren- tiation of native python.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Autograd: Reverse-mode diﬀeren- tiation of native python

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.292694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f1e1a0a5-7fec-4be4-9f48-f4ebd76a38f8 · outbound

This paper cites Data Driven Governing Equations Approximation Using Deep Neural Networks.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Data Driven Governing Equations Approximation Using Deep Neural Networks

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.794374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dccd1230-7ba3-4703-a463-d023805528f5 · outbound

This paper cites Hidden physics models: Machine learning of nonlinear partial diﬀerential equations.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Hidden physics models: Machine learning of nonlinear partial diﬀerential equations

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.276391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9d1daddc-fad7-47b2-9ff7-19033b99f7bd · outbound

This paper cites Machine learning of linear diﬀerential equations using Gaussian processes.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Machine learning of linear diﬀerential equations using Gaussian processes

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.259617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f4a80fec-9432-4362-a0e1-e1c8d4ca73b1 · outbound

This paper cites Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.808547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bab5bb57-534f-4d1c-8f0e-af469e272ca4 · outbound

This paper cites Data-driven discovery of partial diﬀerential equations.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Data-driven discovery of partial diﬀerential equations

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.813692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9c04174-c4f1-4819-8106-e6e692e3114c · outbound

This paper cites Deep neural networks motivated by partial diﬀerential equa- tions.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Deep neural networks motivated by partial diﬀerential equa- tions

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.232445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 02427e11-48e7-4025-92b2-a1bbe5f8a078 · outbound

This paper cites Weight normalization: A simple reparameterization to accelerate training of deep neural networks.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Weight normalization: A simple reparameterization to accelerate training of deep neural networks

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.822940Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9e459d7-fd21-4ea4-9eea-fd7f59230642 · outbound

This paper cites Learning partial diﬀerential equations via data discovery and sparse opti- mization.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Learning partial diﬀerential equations via data discovery and sparse opti- mization

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.205818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7fb1d4b0-3f01-4cdb-a308-4f8b89c97302 · outbound

This paper cites Sparse model selection via integral terms.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Sparse model selection via integral terms

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.189542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b7f8fc98-379c-48e9-b070-3e6c71a6fde1 · outbound

This paper cites Learning Dynamical Systems and Bifurcation via Group Sparsity.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Learning Dynamical Systems and Bifurcation via Group Sparsity

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.838101Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 701141fa-dd6a-4c37-99eb-e60951faf679 · outbound

This paper cites Extracting sparse high-dimensional dynamics from limited data.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Extracting sparse high-dimensional dynamics from limited data

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.172745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9596fe22-8191-4c35-8123-9b71890b192e · outbound

This paper cites Dynamic Mode Decomposition of numerical and experi- mental data.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Dynamic Mode Decomposition of numerical and experi- mental data

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.154566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d81442c1-a201-48df-aac8-cfc5c30f9ee4 · outbound

This paper cites Dynamic mode decomposition of numerical and experimental data.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Dynamic mode decomposition of numerical and experimental data

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.138236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e597cfb5-4760-4b34-ba3d-743c91cb635a · outbound

This paper cites The pi-sigma network: An eﬃcient higher-order neural network for pattern classiﬁcation and function approximation.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data The pi-sigma network: An eﬃcient higher-order neural network for pattern classiﬁcation and function approximation

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.121933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4a396750-e5ea-4b78-89ac-c2d92caab0f9 · outbound

This paper cites Exact recovery of chaotic systems from highly corrupted data.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Exact recovery of chaotic systems from highly corrupted data

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.105896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5b414dcf-819f-4e18-b212-d36bad200a1d · outbound

This paper cites Forward Stability of ResNet and Its Variants.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Forward Stability of ResNet and Its Variants

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-14T14:26:32.867870Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc18130d-8c5d-4c11-8844-614448a1d003 · outbound

This paper cites On the convergence of the sindy algorithm.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data On the convergence of the sindy algorithm

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:26:33.088660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

No inbound Pith citation observations are available.