Paper Citation Record · LEDGER

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications

As of 16 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:1908.10407.

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

pith.paper-citation-record.v1
1908.10407 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T10:51:23.119052Z

measured 38 of 38 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 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

38 of 38 outbound references displayed

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External citation measurements

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Outbound references

Observation 65eb77c4-0f58-4ba5-9c1f-8160591aaa96 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.771063Z

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Observation c9adefb0-49e0-4db2-9256-e4fc9fa3ebd7 · outbound

This paper cites Huerta, T.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Huerta, T

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:51:23.753274Z

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Observation 9aff166f-a89a-4d5f-aa7d-fbcf0a33e45e · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.735638Z

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Observation ab0cc598-fe88-43d0-be68-9474c30aedaa · outbound

This paper cites Goodfellow, Y.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Goodfellow, Y

Reference 4

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Observation 5a1e3c48-a192-4760-9e9f-3775abae0b78 · outbound

This paper cites Abadi, P.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Abadi, P

Reference 5

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Observation c38a9964-d45b-477a-a558-04b8fb38b604 · outbound

This paper cites Ketkar, Introduction to pytorch, in: Deep learning with python, Springer, 2017, pp.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Ketkar, Introduction to pytorch, in: Deep learning with python, Springer, 2017, pp

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:51:23.681790Z

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Observation 17c7ee4e-40b6-464b-acfa-6a211ec70655 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.664268Z

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Observation b58d93d8-23fc-49ab-9024-24b6a954f0e1 · outbound

This paper cites Raissi, Deep hidden physics models: Deep learning of nonlinear partial diﬀerential equations, The Journal of Machine Learning Research 19 (1) (2018) 932–955.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Raissi, Deep hidden physics models: Deep learning of nonlinear partial diﬀerential equations, The Journal of Machine Learning Research 19 (1) (2018) 932–955

Reference 8

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Observation 5df36f1a-c945-411e-8e0d-298214fb0204 · outbound

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

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 9

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Observation c1566676-98ce-4a22-a233-6ee7bb63e628 · outbound

This paper cites Dacorogna, Introduction to the Calculus of Variations, World Scientiﬁc Publishing Company, 2014.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Dacorogna, Introduction to the Calculus of Variations, World Scientiﬁc Publishing Company, 2014

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:51:23.631977Z

Source-reported events for the cited work

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Observation 8ac4147e-0cb7-4f3d-8ed5-207ad5fa9f65 · outbound

This paper cites Baiges, R.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Baiges, R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:51:23.615426Z

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Observation c6933d78-b6c2-4dfa-be55-e8d50cad0109 · outbound

This paper cites Kirchdoerfer, M.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Kirchdoerfer, M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:51:23.598902Z

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Observation 3301ca1a-cc3e-47f3-80b8-02d567c25bd4 · outbound

This paper cites Deep Neural Networks Motivated by Partial Differential Equations.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Deep Neural Networks Motivated by Partial Differential Equations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-14T10:51:22.991585Z

Source-reported events for the cited work

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Observation 21c8fe20-ddcd-41d6-86dc-bfde06ef55cc · outbound

This paper cites Weinan, B.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Weinan, B

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-14T10:51:22.996738Z

Source-reported events for the cited work

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Observation 4a5c9bb0-189a-4f5b-93bc-890f34208181 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.571713Z

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Observation e75c8e2b-4625-4e44-b998-a5f5db8b83c6 · outbound

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

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Topological properties of the set of functions generated by neural networks of fixed size

Reference 16

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Observation 2965c47c-6dd9-4e31-bf1f-398d046b20e8 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.556254Z

Source-reported events for the cited work

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Observation 301d6142-6880-446b-a1f7-f6553663038e · outbound

This paper cites Glorot, Y.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Glorot, Y

Reference 18

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Observation 32dff1fc-5379-4836-bf3c-003db8097d03 · outbound

This paper cites TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems

Reference 19

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Observation c4af7f5f-767c-4080-b231-a8eab348b8fc · outbound

This paper cites ReLU Deep Neural Networks and Linear Finite Elements.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications ReLU Deep Neural Networks and Linear Finite Elements

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-14T10:51:23.026701Z

Source-reported events for the cited work

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Observation d0d00aca-e4db-49c1-82f9-72ecc7100766 · outbound

This paper cites Opschoor, P.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Opschoor, P

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:51:23.525348Z

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Observation 0ebd0dc2-c7a8-4baa-bbe3-dd48739c1caf · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.509880Z

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Observation bf18657d-deda-4e70-af81-f342555464db · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.494239Z

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Observation 408a72dc-f8f9-49dc-922a-d7a7dfd1cac0 · outbound

This paper cites Enhancing approximation abilities of neural networks by training derivatives.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Enhancing approximation abilities of neural networks by training derivatives

Reference 24

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Observation 10835d1f-18a8-4c99-966d-bb50351a5c82 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.478249Z

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Observation c3e8684d-63bd-4b72-8f57-27b7ee9620a6 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.462881Z

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Observation 2d814cb6-8cef-4ae0-ae28-9013761dd4a0 · outbound

This paper cites Schillinger, J.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Schillinger, J

Reference 27

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Observation cff2c541-0a07-47e6-a39e-abd9f2d703df · outbound

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An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 28

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Observation c884b987-89b2-4358-b22e-96f661e8a35d · outbound

This paper cites Logg, K.-A.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Logg, K.-A

Reference 29

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Observation 2cdbcf54-ffe7-40f8-b6f6-a193076b666a · outbound

This paper cites Bourdin, G.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Bourdin, G

Reference 30

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This paper cites Griﬃth, The Phenomena of Rupture and Flow in Solids, Philisophical Transactions of the Royal Society of London 221 (Series A) (1921) 163–198.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Griﬃth, The Phenomena of Rupture and Flow in Solids, Philisophical Transactions of the Royal Society of London 221 (Series A) (1921) 163–198

Reference 31

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Observation e4ef2bae-a878-4d9b-a875-1723445c154e · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.377011Z

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Observation d57565c2-737e-4268-a41e-867c73577bf5 · outbound

This paper cites Miehe, F.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Miehe, F

Reference 33

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Observation 3bff8e7f-7961-464a-9ad8-4ef2edb913ba · outbound

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An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Miehe, M

Reference 34

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Observation 84917d83-8d81-48b3-ae52-f7be1453aa67 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

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Observation 939d81ef-ddc4-4732-89f8-920a48c7bc72 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 36

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Observation 59dd8454-1202-406a-ae5e-4563440344a8 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:51:23.341035Z

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Observation 96708964-3156-42f6-973f-b66d79402100 · outbound

This paper cites an unresolved cited work.

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications Unresolved cited work

Reference 118

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Pith citing papers

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