Paper Citation Record · LEDGER

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems

As of 22 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2505.24578.

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

pith.paper-citation-record.v1
2505.24578 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:28:03.381908Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

40 of 40 outbound references displayed

verified exact1
verified fuzzy29
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5184fa11-0d68-4b9f-8b09-373914f31005 · outbound

This paper cites Piezoelec- tric materials for controlling electro-chemical processes,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Piezoelec- tric materials for controlling electro-chemical processes,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:08.762610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2eb68d29-a356-4949-9f62-98c8f30e0cc6 · outbound

This paper cites Piezoelectric materials for sus- tainable building structures: Fundamentals and applications,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Piezoelectric materials for sus- tainable building structures: Fundamentals and applications,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:08.562436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 902f7b37-a2d7-4429-bc84-b5168fe1f1c6 · outbound

This paper cites A review on applications of piezoelectric materials in aerospace industry,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems A review on applications of piezoelectric materials in aerospace industry,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:08.312696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0b9cef8e-e417-41fa-98d2-013cb6bfc23a · outbound

This paper cites Applications of piezoelectric materials in biomedical engineering,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Applications of piezoelectric materials in biomedical engineering,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:08.098673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e32f6212-4c2d-4072-9245-467e2874a1f7 · outbound

This paper cites A review on piezoelectric materials and their appli- cations,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems A review on piezoelectric materials and their appli- cations,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:07.908176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 096c7b4e-1b6f-422d-8aad-c3440957352f · outbound

This paper cites Hysteresis in piezoelectric and ferroelectric materials,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Hysteresis in piezoelectric and ferroelectric materials,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:07.715644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 063aa39c-015a-4e76-b0fa-c3aeed78a7e1 · outbound

This paper cites Adaptive estimated inverse output-feedback quantized control for piezoelectric positioning stage,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Adaptive estimated inverse output-feedback quantized control for piezoelectric positioning stage,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:07.574498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 717bc429-2f04-42f7-87df-106f3de9d65b · outbound

This paper cites Piezoelectric hysteresis analysis and loss separation,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Piezoelectric hysteresis analysis and loss separation,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:07.359552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 564ebaf0-c3d1-479c-a186-feff3593b5e1 · outbound

This paper cites ¨Uber die magnetische nachwirkung,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems ¨Uber die magnetische nachwirkung,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:07.167722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9d9a6c23-5013-4fff-b48d-939114b3670f · outbound

This paper cites an unresolved cited work.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:28:06.974721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7e5b11ef-1327-4cbc-bc48-5a52ca17c10b · outbound

This paper cites Mag- netic hysteresis modeling with neural operators,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Mag- netic hysteresis modeling with neural operators,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:06.852573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8fa0a298-7c0a-4d77-84cf-5b616fda6721 · outbound

This paper cites A survey on hysteresis modeling, identification and control,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems A survey on hysteresis modeling, identification and control,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:06.687315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d1bd0924-5d3c-431a-bcb7-24c2814ddca5 · outbound

This paper cites Deep learning,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Deep learning,

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:00.908552Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fca78b5a-c2d7-450b-9955-c02177baef27 · outbound

This paper cites Long short-term memory,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Long short-term memory,

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:01.005595Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef48bfa1-3ec7-4b7f-a8a5-b4823787811d · outbound

This paper cites Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:01.090457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b2ad8b3-40f6-4827-bdc4-82184cd41690 · outbound

This paper cites Adaptive neural control for hysteretic nonlinear systems with hysteresis neural direct inverse compensator and its application,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Adaptive neural control for hysteretic nonlinear systems with hysteresis neural direct inverse compensator and its application,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:06.554595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4673e52d-ffa8-4006-b6e5-c917dcf6a21f · outbound

This paper cites Generalizable models of magnetic hys- teresis via physics-aware recurrent neural networks,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Generalizable models of magnetic hys- teresis via physics-aware recurrent neural networks,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:06.429741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 325038ca-2b29-4c3c-86c6-014ec8438601 · outbound

This paper cites Characterizing nonlinear piezoelectric dynamics through deep neural operator learning,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Characterizing nonlinear piezoelectric dynamics through deep neural operator learning,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:06.293815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6c68b774-6c92-4da0-b240-0865d991586a · outbound

This paper cites Neural operator: Learning maps be- tween function spaces with applications to PDEs,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Neural operator: Learning maps be- tween function spaces with applications to PDEs,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:06.187205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7efd7cd5-22c8-4ecc-ac6d-55b57361cf09 · outbound

This paper cites Neural operators for accelerating scientific simu- lations and design,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Neural operators for accelerating scientific simu- lations and design,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:06.081845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3526865f-f15e-4444-b76e-ae0361d2994c · outbound

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

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:05.978605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 042ede6a-b976-4b07-9837-4710cd1567f8 · outbound

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

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Fourier neural operator for parametric partial differential equations,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:05.835447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 85d04c2c-2f79-484b-94dc-0f823ed6ee9b · outbound

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

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Convolutional neural operators for robust and accurate learning of PDEs,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:05.745015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5f208512-a61d-48e8-a93f-28688c6a33fa · outbound

This paper cites Discovery of sparse hysteresis models for piezoelectric materials,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Discovery of sparse hysteresis models for piezoelectric materials,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:05.600014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ff9c8b88-c6d1-41dc-aa1e-09e5369fe25b · outbound

This paper cites Identifi- cation of Bouc–Wen hysteretic systems based on a joint optimization approach,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Identifi- cation of Bouc–Wen hysteretic systems based on a joint optimization approach,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:05.419719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 57940fbb-1184-4912-8042-32d5e31f38b6 · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed deep- onets,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Learning the solution operator of parametric partial differential equations with physics-informed deep- onets,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:05.250100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 25903808-025d-48e8-9c46-71a80b912bf1 · outbound

This paper cites Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:02.281195Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 353fda15-1c76-45d0-a133-e3f2668b0f1f · outbound

This paper cites Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:02.348867Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e10eeae-0bb1-412c-82d4-6a0f7ca9f56d · outbound

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

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Discovering governing equations from data by sparse identification of nonlinear dynamical systems,

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:02.457513Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5ae5da0-1059-44dc-b9a5-0c6e7e7bd463 · outbound

This paper cites Discovering symbolic models from deep learn- ing with inductive biases,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Discovering symbolic models from deep learn- ing with inductive biases,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:05.067920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d2396091-a6d7-4fc5-b16a-95b94df256bc · outbound

This paper cites Why are some hysteresis loops shaped like a butterfly?.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Why are some hysteresis loops shaped like a butterfly?

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:04.889657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8651bb50-79f9-4f02-a961-1d2af40f0245 · outbound

This paper cites Fourier neural operators for arbitrary resolution climate data downscaling,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Fourier neural operators for arbitrary resolution climate data downscaling,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:04.726951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 95195e29-bb77-44be-9e36-ababe6a64bbd · outbound

This paper cites Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators,

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:04.524525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a885edc2-0514-4a65-b3bf-0abcb60cd03e · outbound

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

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Data-driven discovery of partial differential equations,

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:04.331866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 18757d58-0bf9-4b32-93aa-2dd12ece08ac · outbound

This paper cites Regression shrinkage and selection via the lasso,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Regression shrinkage and selection via the lasso,

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:02.968259Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32603b99-8a87-45c9-97b4-b908940595b1 · outbound

This paper cites Ensemble- SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Ensemble- SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control,

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:04.159535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation bdcf4906-9d04-41f2-996d-6e10e6dc193c · outbound

This paper cites Derivative-based SINDy (DSINDy): Address- ing the challenge of discovering governing equations from noisy data,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Derivative-based SINDy (DSINDy): Address- ing the challenge of discovering governing equations from noisy data,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:28:04.042841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f2b8a9d9-1749-4223-87f8-6b34217106cb · outbound

This paper cites Dynamic hysteresis model of grain-oriented ferromagnetic material using neural operators,.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Dynamic hysteresis model of grain-oriented ferromagnetic material using neural operators,

Reference 38

Resolution: verified exact; raw_fallback, observed 2026-08-07T12:28:03.783118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 243abd67-6335-495b-a451-46d4e01c46d5 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Adam: A Method for Stochastic Optimization

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:03.260521Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4af9125-74b8-4d4f-a197-6592c5008168 · outbound

This paper cites an unresolved cited work.

Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Unresolved cited work

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:03.381908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.