Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:21:39.658988Z
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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.