Paper Citation Record · LEDGER

A Neural Operator-Based Approach to Symbolic Discovery of PDEs

As of 22 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 2 inbound Pith citation observations for arXiv:2501.08086.

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

pith.paper-citation-record.v1
2501.08086 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:34:25.149924Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-15T12:27:15.229823Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T08:48:02.531129Z

Reference resolution

30 of 30 outbound references displayed

verified exact1
verified fuzzy18
unresolved11
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bebd7e1f-9218-43fb-aeb5-ab84621c822c · outbound

This paper cites Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.035376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1015b71e-6e21-4dcd-ad41-fea94e972a2a · outbound

This paper cites End-to-end symbolic regression with transformers.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs End-to-end symbolic regression with transformers

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.522269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation df18b0ad-65c9-4f62-ab5b-8243f7ab7324 · outbound

This paper cites Neural symbolic regression that scales.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Neural symbolic regression that scales

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.044371Z

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Unavailable: canonical work link unavailable.

Observation b3f24999-1c8d-4958-9355-1b4e9fb56fa4 · outbound

This paper cites Interactive Symbolic Regression through Offline Reinforcement Learning: A Co-Design Framework.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Interactive Symbolic Regression through Offline Reinforcement Learning: A Co-Design Framework

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-10T20:34:25.232763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation be9d0fd8-e33e-46d9-8ed6-ce4683e1a1f9 · outbound

This paper cites Symformer: End-to-end symbolic regression using transformer-based architecture.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Symformer: End-to-end symbolic regression using transformer-based architecture

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.498968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ea4cf933-5e25-4505-a7b4-b9c0c05e9ff4 · outbound

This paper cites Contemporary symbolic regression methods and their relative performance.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Contemporary symbolic regression methods and their relative performance

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.485877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9f47f559-3e6b-40ad-aef6-ffca019c65e9 · outbound

This paper cites Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.061277Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3446f3c-8e73-4ea6-a2e3-2a00f5543bd5 · outbound

This paper cites Genetic programming as a means for programming computers by natural selection.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Genetic programming as a means for programming computers by natural selection

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.065323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 279accdc-92bc-4e80-a4dd-ddaa784b2bae · outbound

This paper cites Analytical modeling of exoplanet transit spectroscopy with dimensional analysis and symbolic regression.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Analytical modeling of exoplanet transit spectroscopy with dimensional analysis and symbolic regression

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.463758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 75eff6cd-c10b-4078-b911-c51cff60377f · outbound

This paper cites Orbital anomaly reconstruction using deep symbolic regression.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Orbital anomaly reconstruction using deep symbolic regression

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.449388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ac088179-3456-4d2c-afea-f41328dbfb4a · outbound

This paper cites Simple descriptor derived from symbolic regression accelerating the discovery of new perovskite catalysts.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Simple descriptor derived from symbolic regression accelerating the discovery of new perovskite catalysts

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.436573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 99c63359-f74c-42e1-822b-662f6cade8c4 · outbound

This paper cites Machine learning and symbolic regression investigation on stability of mxene materials.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Machine learning and symbolic regression investigation on stability of mxene materials

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.423408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3559ab1f-8e08-4010-811b-5823ddcd4bc1 · outbound

This paper cites Machine learning to guide the use of adjuvant therapies for breast cancer.Nature Machine Intelligence, 3(8):716–726, 2021.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Machine learning to guide the use of adjuvant therapies for breast cancer.Nature Machine Intelligence, 3(8):716–726, 2021

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.410740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5be94956-b472-44bf-82b4-66a1fff90586 · outbound

This paper cites Hemoglobin and glucose level estimation from ppg characteristics features of fingertip video using mggp-based model.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Hemoglobin and glucose level estimation from ppg characteristics features of fingertip video using mggp-based model

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.398135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5307aa82-f94a-45d8-a922-7ceeddd591d6 · outbound

This paper cites Artificial intelligence in physical sci- ences: Symbolic regression trends and perspectives.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Artificial intelligence in physical sci- ences: Symbolic regression trends and perspectives

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.092051Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf923445-e833-47f6-81cb-143a9cdfa4a5 · outbound

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

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Discovering governing equations from data by sparse identification of nonlinear dynamical systems

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.095771Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 781a0a7f-343b-4041-83bc-7d1c97e4f308 · outbound

This paper cites A review of data-driven discovery for dynamic systems.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs A review of data-driven discovery for dynamic systems

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.371358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3a8aef6b-8611-4967-8ea0-2c27f0d362a1 · outbound

This paper cites Learning equations for extrapolation and control.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Learning equations for extrapolation and control

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.102789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5eb35fd0-7895-4d83-b8c8-24499df17068 · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs KAN: Kolmogorov-Arnold Networks

Reference 19

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 65668475-8e25-4d4b-b37d-6f2416da9232 · outbound

This paper cites Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.110794Z

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Unavailable: canonical work link unavailable.

Observation ca9301d1-52e2-4dc7-8677-a8728b60fbb2 · outbound

This paper cites Kan-odes: Kolmogorov–arnold network ordinary differen- tial equations for learning dynamical systems and hidden physics.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Kan-odes: Kolmogorov–arnold network ordinary differen- tial equations for learning dynamical systems and hidden physics

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.351449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 330a9998-8da5-4b2a-9bb2-a47320ae38ba · outbound

This paper cites Learning nonlin- ear operators via deeponet based on the universal approximation theorem of operators.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Learning nonlin- ear operators via deeponet based on the universal approximation theorem of operators

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.338911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 680fa3c5-64d9-4a6c-96f9-0b51a126babe · outbound

This paper cites Convolutional neural operators for robust and accurate learning of pdes.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Convolutional neural operators for robust and accurate learning of pdes

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.327126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d4148e8f-706e-49c0-a07c-371923d50e20 · outbound

This paper cites Laplace neural operator for solving differential equations.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Laplace neural operator for solving differential equations

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.314198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aaf0a4eb-e81e-4238-aea7-f985366857fc · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Fourier Neural Operator for Parametric Partial Differential Equations

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.130596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a67a75b7-b7ef-4351-816c-9dd93e8b71d2 · outbound

This paper cites Semantically-based crossover in genetic programming: application to real-valued symbolic regression.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Semantically-based crossover in genetic programming: application to real-valued symbolic regression

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.301956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4ae3b074-6029-4566-991a-93e1559a48a5 · outbound

This paper cites Improving symbolic regression with interval arithmetic and linear scaling.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Improving symbolic regression with interval arithmetic and linear scaling

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.289827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 36212973-a70a-4f7d-99c0-1b650a2f2602 · outbound

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

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Neural operator: Learning maps between function spaces with applications to pdes

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T20:34:25.142436Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fdbd862-be59-4986-93ac-b45ad6ca3be8 · outbound

This paper cites Learning integral operators via neural integral equations.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Learning integral operators via neural integral equations

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.270271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a1bfdebb-7003-4bba-87b5-bf7476ad8eb8 · outbound

This paper cites Neural networks for machine learning.

A Neural Operator-Based Approach to Symbolic Discovery of PDEs Neural networks for machine learning

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:34:25.257976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation 31045e51-b5ad-47c8-9c6a-a3971968b9e2 · inbound

Neuro-Symbolic ODE Discovery with Latent Grammar Flow cites this paper.

Neuro-Symbolic ODE Discovery with Latent Grammar Flow A Neural Operator-Based Approach to Symbolic Discovery of PDEs

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-06-23T04:13:38.030283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f127cfe5-d44d-4a0b-b124-1a18c829bc00 · inbound

Neuro-Symbolic ODE Discovery with Latent Grammar Flow cites this paper.

Neuro-Symbolic ODE Discovery with Latent Grammar Flow A Neural Operator-Based Approach to Symbolic Discovery of PDEs

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-15T12:27:15.229823Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.