Paper Citation Record · LEDGER

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations

As of 17 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2507.18332.

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

pith.paper-citation-record.v1
2507.18332 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:21:39.658988Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

verified exact4
verified fuzzy31
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation efcb0bbb-0578-4aef-b642-86e11af1227b · outbound

This paper cites Scientific discovery in the age of artificial intelligence[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Scientific discovery in the age of artificial intelligence[J]

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.347094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c8225fd9-89db-4490-8161-523dc920439e · outbound

This paper cites Machine learning for fluid mechanics[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Machine learning for fluid mechanics[J]

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.334469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c4a4f14c-f078-41ce-bc3b-8c514cb8045f · outbound

This paper cites Prospect of artificial intelligence empowered fluid mechanics[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Prospect of artificial intelligence empowered fluid mechanics[J]

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.321486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 489f6c02-9bd2-4e9e-89b2-6e067f8e234f · outbound

This paper cites On physically similar systems; illustrations of the use of dimensional equations[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations On physically similar systems; illustrations of the use of dimensional equations[J]

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.308189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cf5ebc13-2d85-4808-8bf8-6d3003196e0d · outbound

This paper cites Data-driven dimensional analysis: algorithms for unique and relevant dimensionless groups.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Data-driven dimensional analysis: algorithms for unique and relevant dimensionless groups

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:21:39.887353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a7f33480-a384-44b6-ac26-0e6ece898b63 · outbound

This paper cites Data-driven discovery of dimensionless numbers and governing laws from scarce measurements[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Data-driven discovery of dimensionless numbers and governing laws from scarce measurements[J]

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.295506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a54bb744-7da4-49fc-879f-90cf35851ca1 · outbound

This paper cites Deep learning[M].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Deep learning[M]

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.280636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9373d3cd-d501-4b55-b357-f58276d957c9 · outbound

This paper cites Artificial intelligence in physical sciences: Symbolic regression trends and perspectives[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Artificial intelligence in physical sciences: Symbolic regression trends and perspectives[J]

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.267232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation aa2c38ee-3eed-4f50-89c5-81e56b2aa6a8 · outbound

This paper cites Interpretable scientific discovery with symbolic regression: a review[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Interpretable scientific discovery with symbolic regression: a review[J]

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.254564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2e57f40b-6557-40ff-8acf-2aa5497900d2 · outbound

This paper cites Scaling laws from statistical data and dimensional analysis.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Scaling laws from statistical data and dimensional analysis

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.241722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0b7d0ad4-3684-44c0-95ab-f33b80caa409 · outbound

This paper cites Active subspace methods in theory and practice: applications to kriging surfaces[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Active subspace methods in theory and practice: applications to kriging surfaces[J]

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.224899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5cdb5fb2-c23f-46dd-bf3b-70f07205a79e · outbound

This paper cites Data-driven dimensional analysis of heat transfer in irradiated particle-laden turbulent flow[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Data-driven dimensional analysis of heat transfer in irradiated particle-laden turbulent flow[J]

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.210072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 112fc0a8-199d-4df3-8d7b-6cdd863cedbe · outbound

This paper cites Clustering dimensionless learning for multiple -physical-regime systems[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Clustering dimensionless learning for multiple -physical-regime systems[J]

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.192676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 54b5e8cb-6e3f-4bb8-bdd8-7b37c9d12260 · outbound

This paper cites Artificial neural network based response surface for data -driven dimensional analysis[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Artificial neural network based response surface for data -driven dimensional analysis[J]

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.178841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 542060c7-b776-4e05-983b-c6cef03017a1 · outbound

This paper cites Data -driven discovery of self -similarity using neural networks[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Data -driven discovery of self -similarity using neural networks[J]

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.163164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4a5edb59-08de-43b6-8349-d3f9f7bfad74 · outbound

This paper cites FIND: A Framework for Discovering Formulas in Data[C]//Proceedings of the AAAI Conference on Artificial Intelligence.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations FIND: A Framework for Discovering Formulas in Data[C]//Proceedings of the AAAI Conference on Artificial Intelligence

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.148913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8f222f0f-9f99-45ae-8480-796162b6cbc8 · outbound

This paper cites Dimensionless learning based on information[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Dimensionless learning based on information[J]

Reference 17

Resolution: verified exact; raw_fallback, observed 2026-08-15T18:21:39.866067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 28a6f91e-bc29-45e4-b3ac-cdf04c97dc99 · outbound

This paper cites Mutual -information-based dimensional learning: Objective algorithms for identification of relevant dimensionless quantities[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Mutual -information-based dimensional learning: Objective algorithms for identification of relevant dimensionless quantities[J]

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.134154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9ad6027c-841b-42ed-9edd-c8fdd08c5ea9 · outbound

This paper cites On the parameter combinations that matter and on those that do not: data -driven studies of parameter (non) identifiability[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations On the parameter combinations that matter and on those that do not: data -driven studies of parameter (non) identifiability[J]

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.119616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 958bc95a-8ac4-48ec-83ad-181da3518ef9 · outbound

This paper cites Dimensionally consistent learning with Buckingham Pi[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Dimensionally consistent learning with Buckingham Pi[J]

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.106465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2839918b-6322-4ff6-a80d-603440dc492b · outbound

This paper cites Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering[J]

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.090757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 43a8d300-b86f-48ae-8d3a-b5215a92a8c5 · outbound

This paper cites Adaptive space transformation: An invariant based method for predicting aerodynamic coefficients of hypersonic vehicles[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Adaptive space transformation: An invariant based method for predicting aerodynamic coefficients of hypersonic vehicles[J]

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.075824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 096e1c17-77f2-4762-bc88-5b91468af255 · outbound

This paper cites Scaling Function Learning: A sparse aerodynamic data reconstruction method for generalizing aircraft shapes.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Scaling Function Learning: A sparse aerodynamic data reconstruction method for generalizing aircraft shapes

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:21:39.748192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cc3b87d2-bb76-4735-88c5-f366e8b9b636 · outbound

This paper cites Distilling free-form natural laws from experimental data[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Distilling free-form natural laws from experimental data[J]

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.062613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 528b6087-f5f4-4346-bb0a-90855721b73e · outbound

This paper cites Gene Expression Programming: a New Adaptive Algorithm for Solving Problems.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Gene Expression Programming: a New Adaptive Algorithm for Solving Problems

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:21:39.725825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 50724c4e-def7-495a-8a49-7aa12b226d23 · outbound

This paper cites Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T18:21:39.603296Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfe7112d-d7db-4f20-8d26-dded88f93a9e · outbound

This paper cites Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.050158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 642b189d-74e9-4d57-8932-a706c91e7407 · outbound

This paper cites an unresolved cited work.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:21:40.037664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1fa8b677-10ca-452d-985d-138dd7db0742 · outbound

This paper cites The influence of the cell inclination on the heat transport and large -scale circulation in liquid metal convection[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations The influence of the cell inclination on the heat transport and large -scale circulation in liquid metal convection[J]

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.024735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b3b46316-3f6e-4c7a-b4ef-a885c90669a0 · outbound

This paper cites Turbulent Rayleigh –Bénard convection in gaseous and liquid He[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Turbulent Rayleigh –Bénard convection in gaseous and liquid He[J]

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:40.009305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2167bf62-74c4-4a28-81ce-bb7dd0fa7c28 · outbound

This paper cites Turbulent convection at high Rayleigh numbers and aspect ratio 4[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Turbulent convection at high Rayleigh numbers and aspect ratio 4[J]

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:39.994983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ead8bf11-2ce9-4ae6-aa3c-538037bb6573 · outbound

This paper cites Scaling in Rayleigh –Bénard convection[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Scaling in Rayleigh –Bénard convection[J]

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:39.982296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation eacd2d79-4f81-4449-93bc-be98bf3fe13a · outbound

This paper cites Laws of flow in rough pipes[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Laws of flow in rough pipes[J]

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:39.971446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 10e97d08-ac9b-4b3d-af36-e4c1a92931c8 · outbound

This paper cites an unresolved cited work.

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:21:39.955895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ba76f843-e171-4a90-80ca-21da63d79310 · outbound

This paper cites Roughness effects in turbulent pipe flow[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Roughness effects in turbulent pipe flow[J]

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:39.942798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 22a5417f-44d6-404e-978e-77ed600cff35 · outbound

This paper cites EBOOK: Fundamentals of Aerodynamics (SI units)[M].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations EBOOK: Fundamentals of Aerodynamics (SI units)[M]

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:39.928731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fdf23f30-2778-4a9c-98b5-833cbf07b3e5 · outbound

This paper cites Two -dimensional subsonic flow of compressible fluids[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations Two -dimensional subsonic flow of compressible fluids[J]

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:39.914934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a337e225-be15-48d3-85a5-44a546cbce1b · outbound

This paper cites AI Feynman: A physics -inspired method for symbolic regression[J].

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations AI Feynman: A physics -inspired method for symbolic regression[J]

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:21:39.901452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.