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Paper Citation Record · LEDGER

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

As of 15 August 2026, this Paper Citation Record lists 100 of 117 outbound references and 0 inbound Pith citation observations for arXiv:2607.23753.

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

pith.paper-citation-record.v1
2607.23753 v1

Coverage vector

measured 100 of 117 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

100 of 117 outbound references displayed

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Outbound references

Observation 897daec2-cedf-4169-9250-acd10cf9e2ab · outbound

This paper cites an unresolved cited work.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Unresolved cited work

Reference 1

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Observation e6a3e57d-3faf-4fc8-b7ef-027dbc926535 · outbound

This paper cites Stuart, and Anima Anandkumar.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Stuart, and Anima Anandkumar

Reference 2

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Observation 63c9e1ec-88ac-449b-bbe5-c6556024b5f0 · outbound

This paper cites Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

Reference 3

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Observation 5a26c61b-a9e5-4438-a105-61775e50947a · outbound

This paper cites Brunton, Joshua L.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Brunton, Joshua L

Reference 4

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Observation 42ad4572-5d34-4ce0-bc74-291f924f6852 · outbound

This paper cites PDE-net: Learning PDEs from data.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement PDE-net: Learning PDEs from data

Reference 5

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Observation 659751ed-d81e-4777-b505-9372b20ecde8 · outbound

This paper cites A Robust SINDy Approach by Combining Neural Networks and an Integral Form.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement A Robust SINDy Approach by Combining Neural Networks and an Integral Form

Reference 6

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Observation fd99b6e5-1e5c-444c-836b-3d3e5fc8c80e · outbound

This paper cites Pde-learn: Using deep learning to discover partial differential equations from noisy, limited data.Neural Networks, 174:106242, 2024.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Pde-learn: Using deep learning to discover partial differential equations from noisy, limited data.Neural Networks, 174:106242, 2024

Reference 7

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Observation 05f38231-0cbd-403c-a820-4e2c430bf237 · outbound

This paper cites Unrolled-sindy: A stable explicit method for non linear pde discovery from sparsely sampled data.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Unrolled-sindy: A stable explicit method for non linear pde discovery from sparsely sampled data

Reference 8

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Observation 365d0057-52aa-4f01-8995-98ec7aff0c0a · outbound

This paper cites PhysPDE: Rethinking PDE discovery and a physical HYpothesis selection benchmark.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement PhysPDE: Rethinking PDE discovery and a physical HYpothesis selection benchmark

Reference 9

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Observation 73d6927b-aa1b-4b27-b2dc-bddef73876dc · outbound

This paper cites Nathan Kutz, and Steven L.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Nathan Kutz, and Steven L

Reference 10

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Observation f83acc1f-6665-437c-b2b6-efd24f466ef0 · outbound

This paper cites Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion.Research, 6, January 2023.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion.Research, 6, January 2023

Reference 11

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Observation 10b79d93-2537-4a89-af47-0e31a37978ac · outbound

This paper cites Mdbench: Bench- marking data-driven methods for model discovery.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Mdbench: Bench- marking data-driven methods for model discovery

Reference 12

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Observation 4e5dfc3d-9222-4794-b127-2545fd09a7ca · outbound

This paper cites Ap- proximation Error of Sobolev Regular Functions with tanh Neural Networks: Theoretical Impact on PINNs.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Ap- proximation Error of Sobolev Regular Functions with tanh Neural Networks: Theoretical Impact on PINNs

Reference 13

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Observation 201af8e5-3aee-4cd9-beca-a0d0f98f7ce7 · outbound

This paper cites Error estimates for physics-informed neural networks approximating the navier–stokes equations.IMA Journal of Numerical Analysis, 44(1):83–119, 02 2024.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Error estimates for physics-informed neural networks approximating the navier–stokes equations.IMA Journal of Numerical Analysis, 44(1):83–119, 02 2024

Reference 14

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Observation a692386e-6cbd-4351-8ec0-6da1aaa3d806 · outbound

This paper cites On the convergence of PINNs.Bernoulli, 31(3):2127 – 2151, 2025.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement On the convergence of PINNs.Bernoulli, 31(3):2127 – 2151, 2025

Reference 15

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Observation bf7f9145-cf31-4e81-bb1a-c2330bc624e5 · outbound

This paper cites Miettinen.Nonlinear multiobjective optimization.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Miettinen.Nonlinear multiobjective optimization

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Observation fd41541d-8894-4c18-bced-3d7e7477837b · outbound

This paper cites Ro- drigues.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Ro- drigues

Reference 17

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Observation 69ec4d9c-393c-454a-8364-edc7cf641555 · outbound

This paper cites Data-driven discovery of governing differential equations across physical systems.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Data-driven discovery of governing differential equations across physical systems

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Lagergren, John T

Reference 19

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Mechanistic PDE networks for dis- covery of governing equations

Reference 20

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Observation 78baf555-a708-40d2-a425-74863cb2e057 · outbound

This paper cites Data-driven discovery of PDEs via the adjoint method.Transactions on Machine Learning Research, 2025.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Data-driven discovery of PDEs via the adjoint method.Transactions on Machine Learning Research, 2025

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Observation 2d5cdc89-3803-43a8-9821-9a46caa78748 · outbound

This paper cites On the stability of feature selection algorithms.Journal of Machine Learning Research, 18(174):1–54, 2018.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement On the stability of feature selection algorithms.Journal of Machine Learning Research, 18(174):1–54, 2018

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Observation d9cc9dd0-7049-4505-8682-a8185b0bde78 · outbound

This paper cites Learning sparse nonlinear dynamics via mixed-integer optimization.Nonlinear Dynamics, 7(11), 2022.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Learning sparse nonlinear dynamics via mixed-integer optimization.Nonlinear Dynamics, 7(11), 2022

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Observation 53ddbad4-746d-46b4-91d1-668ab4e6bb76 · outbound

This paper cites Tanimoto random features for scalable molecular machine learning.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Tanimoto random features for scalable molecular machine learning

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Observation 2524fcab-202a-454b-96cf-10af8dd71d9f · outbound

This paper cites Dynamic bayesian optimization framework for instruction tuning in partial differential equation discovery.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Dynamic bayesian optimization framework for instruction tuning in partial differential equation discovery

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Observation 19de78c9-1783-4296-b968-1044245ebcad · outbound

This paper cites Data-driven discovery of dynamical systems in pharmacology using large language models.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Data-driven discovery of dynamical systems in pharmacology using large language models

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This paper cites Foundation models for equation discovery in high energy physics.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Foundation models for equation discovery in high energy physics

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Unresolved cited work

Reference 28

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Observation a6fa53da-ee89-49a8-9b05-a7252756b6ec · outbound

This paper cites Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Messenger and David M

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Observation 358096c3-01b9-4108-a71e-74a6aca34e11 · outbound

This paper cites Fasel, J.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Fasel, J

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Observation a26052e8-059c-440f-8b3a-7c9ffcf6201c · outbound

This paper cites Callaghan, and Dongxiao Zhang.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Callaghan, and Dongxiao Zhang

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Observation 5752a8ba-8310-4f89-af56-a38006429d31 · outbound

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Discovering symbolic partial differ- ential equation by abductive learning

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Observation 1021c8ad-691f-4b3b-8905-a7afdfff93f8 · outbound

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Learning gradient flow: Using equation discovery to accelerate engineering optimization.Computer Methods in Applied Mechanics and Engineering, 460:119099, 2026

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Observation 7e475dd1-0a08-491b-a9f6-46ff5fccfb37 · outbound

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Observation e17e6929-de2f-41d0-9379-8fcea54f1964 · outbound

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Evaluating PDE discovery methods for multiscale modeling of biological signals

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Observation f2743ef8-ef7d-49bb-b424-d263284c3ef0 · outbound

This paper cites J¨ arvelin and J.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement J¨ arvelin and J

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source=pdf_text observed=2026-07-30T13:41:05.331546Z digest=sha256:4470426b9af55beda684e04317f1ba3a731188006537ba422fcbf0a4b91be917

Observation 8ef41b3d-2870-4190-ae45-95d33d09d417 · outbound

This paper cites Nexus: A revolutionary framework for autonomous equation discovery.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Nexus: A revolutionary framework for autonomous equation discovery

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Observation 0ffae51b-0d6c-4d16-b1fd-3cde01ec58ec · outbound

This paper cites Holden and N.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Holden and N

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source=pdf_text observed=2026-07-30T13:41:05.521461Z digest=sha256:7ee4ff38695496a36c441dd0dd3cf986c7e68d3be55164a4e6c7435aff2782af

Observation 51b90e67-946c-4cba-9534-8823d934ee61 · outbound

This paper cites Hairer, C.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Hairer, C

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source=pdf_text observed=2026-07-30T13:41:05.715752Z digest=sha256:48b6aeca9d8c67205f60bf9f48b1c70b1485eb33d0c642db9c5356aeabf05b43

Observation 14f6fad2-db59-4906-a2b9-e96cd68ef9af · outbound

This paper cites Photonic Learning in Ultrafast Laser-Induced Complexity.Ultrafast Sci- ence, March 2026.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Photonic Learning in Ultrafast Laser-Induced Complexity.Ultrafast Sci- ence, March 2026

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source=pdf_text observed=2026-07-30T13:41:05.794500Z digest=sha256:a5aae6012daebb15bfedefee4a3cd2fa2a8324717d800f2268f7b263bdec0a31

Observation c4a33d03-30a6-496b-a0c9-852471c805b5 · outbound

This paper cites Discovery of Nonlinear Dynamics with Automated Basis Function Generation.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Discovery of Nonlinear Dynamics with Automated Basis Function Generation

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source=pdf_text observed=2026-07-30T13:41:05.901696Z digest=sha256:80e945fad364d8d9c65be68ded943e7ecf59f4c72e150ca523a12eea01873c25

Observation 6d42b305-7224-44c8-b1bd-fc401a2f93f7 · outbound

This paper cites Brenner and Larkin R.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Brenner and Larkin R

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source=pdf_text observed=2026-07-30T13:41:06.043715Z digest=sha256:7b62688713d934650a1e43cc366f8727ddbd43fe4d3e6935d31512f91c58940d

Observation 430cd95d-4700-4889-8577-90b676ffbc35 · outbound

This paper cites an unresolved cited work.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Unresolved cited work

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source=pdf_text observed=2026-07-30T13:41:06.119458Z digest=sha256:4b253bc5c9f30f5d9b92715efc881f3176bff379d422e44c88cb05bec98be749

Observation f7811e4e-ee65-4561-86f7-3f6612c2b3aa · outbound

This paper cites Latent space symmetry discovery.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Latent space symmetry discovery

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source=pdf_text observed=2026-07-30T13:41:06.196716Z digest=sha256:c4d8e8a49916157ab8f8b3297a61f5059b49a44b36023b035489f3f4473c2cfa

Observation c28de62b-99ef-4c43-a9d0-488363a4abed · outbound

This paper cites an unresolved cited work.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Unresolved cited work

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source=pdf_text observed=2026-07-30T13:41:06.292065Z digest=sha256:922d77e0bb0ebe32dacf0cc1ecec97ca325a40f4b1a7ebefaf02764df2339a7a

Observation 679cbc42-4f52-47ea-aeda-b312f2c4ad1b · outbound

This paper cites Smeulders.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Smeulders

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source=pdf_text observed=2026-07-30T13:41:06.422570Z digest=sha256:970e3bd99e4ee75a12568423f0a91c3671068941a3d614a4cd814ed30d8e3eb0

Observation ed0c6ed4-051e-4e79-a033-447e5bae90fd · outbound

This paper cites Discovering physics laws of dynamical systems via invariant function learning.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Discovering physics laws of dynamical systems via invariant function learning

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source=pdf_text observed=2026-07-30T13:41:06.491382Z digest=sha256:30416f0e75c8e935a36207abe8ece904cedc04018a5f36e7a8645173b1c4773d

Observation 83cc0ad5-b284-42ec-80e4-a695fffbc2d8 · outbound

This paper cites Symmetry-informed governing equation discovery.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Symmetry-informed governing equation discovery

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source=pdf_text observed=2026-07-30T13:41:06.558951Z digest=sha256:f2b63d636a1152591dee2b845f237d8a2b6b1ff0e05169a9b9f83b19640bad49

Observation 8603a2b5-dba6-48c2-a92b-804b446a0b7d · outbound

This paper cites Automatic symme- try discovery with lie algebra convolutional network.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Automatic symme- try discovery with lie algebra convolutional network

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source=pdf_text observed=2026-07-30T13:41:06.637602Z digest=sha256:197d3e0ef5300e8233b41d18f56c4e904f54135289b1a91fc357481892b57942

Observation 3d3437df-7816-4860-94de-8f1cc1887cd6 · outbound

This paper cites Automated discovery of conservation laws via hybrid neural ode-transformers.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Automated discovery of conservation laws via hybrid neural ode-transformers

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source=pdf_text observed=2026-07-30T13:41:06.705072Z digest=sha256:b2695ceb369c99d66229572f1361839e4165b7cf87c5a28c2715f8238c2d33ee

Observation a5f9ebec-3b09-41d6-94ed-a1eda5b13802 · outbound

This paper cites Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation

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source=pdf_text observed=2026-07-30T13:41:06.790601Z digest=sha256:786b7b081cb69c1f60407d7f9b816e1832cb99ea1e3d46b8db5131b1572a2607

Observation d97ea4cb-7a01-4ea3-9f9d-25a56f17e1fb · outbound

This paper cites an unresolved cited work.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Unresolved cited work

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source=pdf_text observed=2026-07-30T13:41:06.861110Z digest=sha256:1e6bacd996ca429c989e40cfd9e8a0d7876cced096b3924651863394548ecae6

Observation 1c50495e-ea97-4c5c-92a7-315fdc2260da · outbound

This paper cites A visual dive into conditional flow matching.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement A visual dive into conditional flow matching

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source=pdf_text observed=2026-07-30T13:41:06.935804Z digest=sha256:f38050f769b8e930f779b31e8aa774d792e6dfdb07864c8c5002e671ad959ce9

Observation a2c5b609-68e8-40f6-9e97-e3404c7ea580 · outbound

This paper cites M´ emoire sur la th´ eorie des d´ eblais et de remblais.Histoire de l’Acad´ emie Royale des Sciences de Paris, page 666–704, 1781.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement M´ emoire sur la th´ eorie des d´ eblais et de remblais.Histoire de l’Acad´ emie Royale des Sciences de Paris, page 666–704, 1781

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source=pdf_text observed=2026-07-30T13:41:07.007734Z digest=sha256:c133a85f23376838299b03e84270971c9f2cd7c169635041cc31351b2909ad36

Observation 2f2788bb-9a4f-4ca3-a459-5e9be6ec0e3f · outbound

This paper cites Sinkhorn distances: Lightspeed computation of optimal transport.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Sinkhorn distances: Lightspeed computation of optimal transport

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source=pdf_text observed=2026-07-30T13:41:07.082585Z digest=sha256:486ec3415fd074db764e16bd3419c8e195e50b4cf994fb19a3629b74c0f05994

Observation 7a242e25-ffe6-4891-815a-00709fe9169c · outbound

This paper cites Wasserstein generative adversarial net- works.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Wasserstein generative adversarial net- works

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source=pdf_text observed=2026-07-30T13:41:07.159140Z digest=sha256:6a003170e8601df76150413120a83a533847f9e937b2135a73d932295c184502

Observation a6988adf-7089-4bd6-8b68-5038c529213c · outbound

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Euclidean, Metric, and Wasserstein gradient flows: an overview.Math

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source=pdf_text observed=2026-07-30T13:41:07.231808Z digest=sha256:f78567aa199b3ef0e69138af1faf729ce19e6b8a0470eb573b24f93bdcba63a8

Observation b51c450f-c54c-476a-881a-dfc291e1ff08 · outbound

This paper cites Peletier, Giuseppe Savar´ e, and Marco Veneroni.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Peletier, Giuseppe Savar´ e, and Marco Veneroni

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source=pdf_text observed=2026-07-30T13:41:07.298145Z digest=sha256:a2bf860edaa60e92d7e9ebdbed310163d1879cbb65d4c1cc96f4da1161f84af4

Observation fe7a9744-e796-4472-99c2-a8a1e0e209a7 · outbound

This paper cites an unresolved cited work.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Unresolved cited work

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source=pdf_text observed=2026-07-30T13:41:07.391607Z digest=sha256:d1f9f4121f9a591b24e3e65681048625ad7087ba46d9796030b7243ff96a04d8

Observation cef8f252-f82d-4215-ba7c-016b78eb719e · outbound

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement A multiscale approach to optimal transport.Computer Graphics Forum, 30:1583 – 1592, 2011 2011

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source=pdf_text observed=2026-07-30T13:41:07.465896Z digest=sha256:abe3e6714e7654a305c3a27388f09651d4daacb693145c02d0dc8a3f0836ce7d

Observation 01e13e4d-f09e-49fb-b355-d0f25e09b80c · outbound

This paper cites Augmented Lagrangian methods for transport optimization, mean field games and degenerate elliptic equations.J.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Augmented Lagrangian methods for transport optimization, mean field games and degenerate elliptic equations.J

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source=pdf_text observed=2026-07-30T13:41:07.541610Z digest=sha256:d293166530efbc4d87af3a23da3c0bb3323f245095e1d8972a0381552e7941be

Pith citing papers

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