Paper Citation Record · LEDGER

Inverse Evolution Data Augmentation for Neural PDE Solvers

As of 23 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2501.14604.

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pith.paper-citation-record.v1
2501.14604 v1

Coverage vector

measured 30 of 30 reference resolution

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measured 30 of 30 standing notices

One-hop event checks from named stored sources.

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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

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Source: cited_works

Reference resolution

30 of 30 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 19d1d93e-adc2-47fa-8816-e968886518da · outbound

This paper cites Representation equiv- alent neural operators: a framework for alias-free operator learning.

Inverse Evolution Data Augmentation for Neural PDE Solvers Representation equiv- alent neural operators: a framework for alias-free operator learning

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:48.155086Z

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Observation 8cb9ce00-a1e1-47eb-977d-27dfc8ea0f8a · outbound

This paper cites An introduction to fluid dynamics.

Inverse Evolution Data Augmentation for Neural PDE Solvers An introduction to fluid dynamics

Reference 2

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Observation 5e1bfcf7-386e-4755-992f-bca52c593f89 · outbound

This paper cites Lie point symmetry data augmentation for neural pde solvers.

Inverse Evolution Data Augmentation for Neural PDE Solvers Lie point symmetry data augmentation for neural pde solvers

Reference 3

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Observation ae02f73e-9785-4774-b9e7-f6166d24b756 · outbound

This paper cites On the partial difference equations of mathematical physics.

Inverse Evolution Data Augmentation for Neural PDE Solvers On the partial difference equations of mathematical physics

Reference 4

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Observation 8f91267f-cc17-46d0-972b-ae4b53193411 · outbound

This paper cites Scientific machine learning through physics–informed neural networks: Where we are and what’s next.

Inverse Evolution Data Augmentation for Neural PDE Solvers Scientific machine learning through physics–informed neural networks: Where we are and what’s next

Reference 5

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Observation 052cd667-4bbc-4d24-a33a-cccd26e960ad · outbound

This paper cites Computational differential equations.

Inverse Evolution Data Augmentation for Neural PDE Solvers Computational differential equations

Reference 6

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Observation f4e6db97-c139-40b6-9628-7d88fe3e4ba4 · outbound

This paper cites Partial differential equations , volume 19.

Inverse Evolution Data Augmentation for Neural PDE Solvers Partial differential equations , volume 19

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:48.064399Z

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Observation 7b07dc89-6221-4dad-aee7-bc8c38db9101 · outbound

This paper cites General covariance data augmentation for neural pde solvers.

Inverse Evolution Data Augmentation for Neural PDE Solvers General covariance data augmentation for neural pde solvers

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:48.049023Z

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Observation ab3f49c3-27bd-4537-96d3-7a3901fdc596 · outbound

This paper cites Towards Multi-spatiotemporal-scale Generalized PDE Modeling.

Inverse Evolution Data Augmentation for Neural PDE Solvers Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 9

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Observation 37e2abe2-a71d-4877-ae09-0759748c9554 · outbound

This paper cites The era5 global reanalysis.

Inverse Evolution Data Augmentation for Neural PDE Solvers The era5 global reanalysis

Reference 10

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Observation 25dc4a00-dd29-456a-bb4f-4a97a2119201 · outbound

This paper cites Adaptive moving mesh methods , volume 174.

Inverse Evolution Data Augmentation for Neural PDE Solvers Adaptive moving mesh methods , volume 174

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:48.018500Z

Source-reported events for the cited work

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Observation 788e5fe7-e96a-4d62-a64d-03f34db3eddc · outbound

This paper cites On univer- sal approximation and error bounds for fourier neural operators.

Inverse Evolution Data Augmentation for Neural PDE Solvers On univer- sal approximation and error bounds for fourier neural operators

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:48.002914Z

Source-reported events for the cited work

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Observation d79e4970-e0ee-43be-a268-ecac5364fe03 · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to pdes.

Inverse Evolution Data Augmentation for Neural PDE Solvers Neural operator: Learning maps between function spaces with applications to pdes

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T15:02:47.600621Z

Source-reported events for the cited work

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Observation 98f40fed-5b8d-4385-8be8-9f1ad6bc83e2 · outbound

This paper cites Partial differential equations and stochastic methods in molecular dynamics.

Inverse Evolution Data Augmentation for Neural PDE Solvers Partial differential equations and stochastic methods in molecular dynamics

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.976821Z

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Observation e7bc1580-a3eb-4e4b-8db9-07f33351b714 · outbound

This paper cites Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems.

Inverse Evolution Data Augmentation for Neural PDE Solvers Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems

Reference 15

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Source-reported events for the cited work

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Observation 622b7d46-c007-488d-9cf3-91e403fd6136 · outbound

This paper cites Physics-guided data augmentation for learning the solution operator of linear differential equations.

Inverse Evolution Data Augmentation for Neural PDE Solvers Physics-guided data augmentation for learning the solution operator of linear differential equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.951215Z

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Observation 439df16f-278f-4505-8eef-37aabdf4add3 · outbound

This paper cites Fourier neural operator for parametric partial differential equations.

Inverse Evolution Data Augmentation for Neural PDE Solvers Fourier neural operator for parametric partial differential equations

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.934404Z

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Observation c6da9037-3cfa-43b6-aaeb-51071ba57d64 · outbound

This paper cites Learning chaotic dynamics in dissipative systems.

Inverse Evolution Data Augmentation for Neural PDE Solvers Learning chaotic dynamics in dissipative systems

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.918922Z

Source-reported events for the cited work

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Observation 643d630f-98bd-490d-9cfb-f3992cc8208c · outbound

This paper cites Physics-informed neural operator for learning partial differential equations.

Inverse Evolution Data Augmentation for Neural PDE Solvers Physics-informed neural operator for learning partial differential equations

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.904187Z

Source-reported events for the cited work

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Observation f6c0b5c8-f0f8-4603-90ec-e2c08c7d2486 · outbound

This paper cites Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks.

Inverse Evolution Data Augmentation for Neural PDE Solvers Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks

Reference 20

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Observation 8667c0c3-5480-4cc1-9fcc-562bff77bc03 · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.

Inverse Evolution Data Augmentation for Neural PDE Solvers Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.888694Z

Source-reported events for the cited work

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Observation f9ac2577-1416-4aef-9fa6-52f175d8f59c · outbound

This paper cites Deep- xde: A deep learning library for solving differential equations.

Inverse Evolution Data Augmentation for Neural PDE Solvers Deep- xde: A deep learning library for solving differential equations

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.872883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7a86a0eb-2cd3-48b4-85fa-c24d9c753c8c · outbound

This paper cites Numerical models for differential problems, volume 2.

Inverse Evolution Data Augmentation for Neural PDE Solvers Numerical models for differential problems, volume 2

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T15:02:47.646083Z

Source-reported events for the cited work

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Observation 5d28f417-8759-4577-b617-c79c20dabc9a · outbound

This paper cites Numerical approximation of partial differential equations, volume 23.

Inverse Evolution Data Augmentation for Neural PDE Solvers Numerical approximation of partial differential equations, volume 23

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-10T15:02:47.650521Z

Source-reported events for the cited work

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Observation 36e04f03-82bc-4210-89b9-eef8a1ccef46 · outbound

This paper cites Physics- informed neural networks: A deep learning framework for solving forward 19 and inverse problems involving nonlinear partial differential equations.

Inverse Evolution Data Augmentation for Neural PDE Solvers Physics- informed neural networks: A deep learning framework for solving forward 19 and inverse problems involving nonlinear partial differential equations

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.835239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 74e36eaf-6d13-4850-a299-5eb7db29317a · outbound

This paper cites Numerical solution of partial differential equations: finite difference methods.

Inverse Evolution Data Augmentation for Neural PDE Solvers Numerical solution of partial differential equations: finite difference methods

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.817890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e9c1f5fd-cb43-419d-8007-69456fd1a629 · outbound

This paper cites Pdebench: An extensive benchmark for scientific machine learning.

Inverse Evolution Data Augmentation for Neural PDE Solvers Pdebench: An extensive benchmark for scientific machine learning

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.802711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 94ebb77d-488c-48cb-a9b2-29e130a75dca · outbound

This paper cites Long-time integration of paramet- ric evolution equations with physics-informed deeponets.

Inverse Evolution Data Augmentation for Neural PDE Solvers Long-time integration of paramet- ric evolution equations with physics-informed deeponets

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.787266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4256d1ae-8843-4b57-9599-6f663649a41c · outbound

This paper cites Learning the solu- tion operator of parametric partial differential equations with physics- informed deeponets.

Inverse Evolution Data Augmentation for Neural PDE Solvers Learning the solu- tion operator of parametric partial differential equations with physics- informed deeponets

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.771732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 106c81f8-d528-4f4a-8710-91e703f2c5e3 · outbound

This paper cites Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges.

Inverse Evolution Data Augmentation for Neural PDE Solvers Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:02:47.756041Z

Source-reported events for the cited work

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Pith citing papers

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