Paper Citation Record · LEDGER

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs

As of 8 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:2506.23024.

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

pith.paper-citation-record.v1
2506.23024 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:01:51.702800Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T23:55:48.420884Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T00:02:49.916838Z

Reference resolution

43 of 43 outbound references displayed

verified exact2
verified fuzzy17
unresolved21
parse uncertain0
malformed identifier2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8749bc87-4ed5-4a2f-88cd-d20a05f6280e · outbound

This paper cites and Trefethen, L.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs and Trefethen, L

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.833351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 98fa3127-a110-4367-9177-9a688682a210 · outbound

This paper cites and Peherstorfer, B.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs and Peherstorfer, B

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.826197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4e2278e3-33e0-44a7-b72c-6dfae1efe127 · outbound

This paper cites and Trefethen, L.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs and Trefethen, L

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:48.055038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 648bde6a-593c-4a25-a2f0-5b67a63c3a67 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:54.819058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c0f25f98-996c-4946-bf43-532c91f40676 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:54.811316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ef42ea25-a69d-408b-acde-c3e9cd23bc9b · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:54.803221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4c2967f3-0273-4a00-82be-7c99dd972e8e · outbound

This paper cites L., Nathan Kutz, J., Manohar, K., Aravkin, A.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs L., Nathan Kutz, J., Manohar, K., Aravkin, A

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.795408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f914c0d6-153a-4398-98d3-32a420845333 · outbound

This paper cites Y ., Quarteroni, A., and Zang, T.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Y ., Quarteroni, A., and Zang, T

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.787850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9cbf7692-0231-4026-9ada-5e2c50fdcfc2 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:54.779794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0d61447b-51fb-4aa5-bdf4-50cd1f900179 · outbound

This paper cites TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:48.763725Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80ba2dfa-b41d-43f9-9bc8-a8b1da043bb4 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:54.771734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 16c67f9b-4c3d-41d5-a5a5-db9e3b8d8801 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 12

Resolution: malformed identifier; no resolver link, observed 2026-08-06T22:01:48.952261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 27252fc5-9d54-4325-9fd6-6d00f34d5f3d · outbound

This paper cites Generation of finite difference formulas on arbitrarily spaced grids.Mathematics of computation, 51(184):699–706, 1988.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Generation of finite difference formulas on arbitrarily spaced grids.Mathematics of computation, 51(184):699–706, 1988

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.764457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6a8143a7-a8b9-40b5-83b7-238c6afb212d · outbound

This paper cites A practical guide to pseudospectral methods.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs A practical guide to pseudospectral methods

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.756725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1ac88bdd-8b63-4889-9650-056a7512a0c0 · outbound

This paper cites Turbulence: the legacy of AN Kolmogorov.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Turbulence: the legacy of AN Kolmogorov

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.748859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation aa84194f-5751-4f1c-99f6-e430daee30aa · outbound

This paper cites Pinnacle: A comprehensive benchmark of physics-informed neural networks for solving pdes,.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Pinnacle: A comprehensive benchmark of physics-informed neural networks for solving pdes,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.741273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6a08089e-b2f0-4fa0-a6f7-d6647f1c5d1f · outbound

This paper cites J.The finite element method: linear static and dynamic finite element analysis.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs J.The finite element method: linear static and dynamic finite element analysis

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.733466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d806ff82-6633-4868-b671-8eb84d1d0f9f · outbound

This paper cites Optimizing a DIscrete Loss (ODIL) to solve forward and inverse problems for partial differential equations using machine learning tools.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Optimizing a DIscrete Loss (ODIL) to solve forward and inverse problems for partial differential equations using machine learning tools

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:01:52.207217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f763567d-642a-42c3-8be0-c212220e2ac6 · outbound

This paper cites Solving inverse problems in physics by optimizing a discrete loss: Fast and accurate learning without neural networks.PNAS nexus, 3(1): pgae005, 2024.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Solving inverse problems in physics by optimizing a discrete loss: Fast and accurate learning without neural networks.PNAS nexus, 3(1): pgae005, 2024

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.725868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 97db5428-3c26-4428-ba3d-888d2658b56b · outbound

This paper cites E., Kevrekidis, I.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs E., Kevrekidis, I

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:54.603095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ed3e6766-7862-412a-a7c3-e6a286c29a62 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Adam: A Method for Stochastic Optimization

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:49.866364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c294caf-d36f-4eb2-a27c-330a88259750 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:54.221319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 45dcc439-5826-4980-85d5-39b5c9e7d3a6 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:53.844517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c30ec140-1bbb-49a4-bc64-51c6df5061f8 · outbound

This paper cites Towards Learning High-Precision Least Squares Algorithms with Sequence Models.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Towards Learning High-Precision Least Squares Algorithms with Sequence Models

Reference 24

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T22:01:52.100038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2d2dcf07-7ede-4d98-b86b-d1743411e948 · outbound

This paper cites L., Gagne, D.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs L., Gagne, D

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:53.545499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3b4a6892-2de9-4cb3-a6b0-1fb41ad74fee · outbound

This paper cites and Hakim, A.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs and Hakim, A

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:50.305433Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 356eddbc-d741-4eef-bf55-1c63828cdcd0 · outbound

This paper cites J., Liu, Z., and Tegmark, M.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs J., Liu, Z., and Tegmark, M

Reference 27

Resolution: verified exact; doi, observed 2026-08-06T22:01:51.859356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0dbf54b9-1c00-4245-8827-458a6b33faf6 · outbound

This paper cites and Molinaro, R.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs and Molinaro, R

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:53.380878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 97c85895-2db7-49b7-8730-8a941bd09d60 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:50.545233Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f33a0ed6-fae8-48e0-afc2-ab6d96bdbb57 · outbound

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

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:50.639812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28b49c76-c61b-4d59-b653-ccf31c3cca1a · outbound

This paper cites Challenges in Training PINNs: A Loss Landscape Perspective.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Challenges in Training PINNs: A Loss Landscape Perspective

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:50.734585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8b1ebdd-76c8-4d9b-837a-d14bb6a95c7a · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:53.229275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0156e35a-e1a5-4081-a840-c6e0b5adda5b · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:50.970210Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6999588b-2c08-40d5-8fe3-ac2866c98202 · outbound

This paper cites an unresolved cited work.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:53.090349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 462924ce-322c-4ab3-9883-d23520155ba3 · outbound

This paper cites High-dimensional probability: An introduction with applications in data science, volume 47.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs High-dimensional probability: An introduction with applications in data science, volume 47

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:51.211163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db350a3f-ec2d-4d7c-9412-787951796b15 · outbound

This paper cites Understanding and mitigating gradient flow pathologies in physics-informed neural networks.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Understanding and mitigating gradient flow pathologies in physics-informed neural networks

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:52.947415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3c4b414c-0c3b-43d4-9f9c-4976ae1cc358 · outbound

This paper cites An Expert's Guide to Training Physics-informed Neural Networks.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs An Expert's Guide to Training Physics-informed Neural Networks

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:51.382494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 297984f6-6cbc-4dca-809c-d560d54ab0eb · outbound

This paper cites Multi-stage Neural Networks: Function Approximator of Machine Precision.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Multi-stage Neural Networks: Function Approximator of Machine Precision

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:51.456449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e88ba0c-f5c9-488b-9f32-552578140ad5 · outbound

This paper cites Turbulence Modeling for CFD.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs Turbulence Modeling for CFD

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:52.784078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 98edb34b-b42e-4374-934b-8e912dd5812d · outbound

This paper cites fixed nodal collocation.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs fixed nodal collocation

Reference 40

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T22:01:52.628396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1e3edc67-b732-42b4-8e48-ff67c1a53bfa · outbound

This paper cites This term accounts for the gap between the best polynomial ap- proximation to the PDE solution, u∗, and the true solution to the numerical surrogate, eu.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs This term accounts for the gap between the best polynomial ap- proximation to the PDE solution, u∗, and the true solution to the numerical surrogate, eu

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:52.477046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dc3338c4-7827-40c2-bab0-fd90a5ed82a9 · outbound

This paper cites This term accounts for the gap between the t-th iterate, u(t) N , and the true solution to the numerical surrogate PDE,eu.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs This term accounts for the gap between the t-th iterate, u(t) N , and the true solution to the numerical surrogate PDE,eu

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:52.338372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0b9cbb66-028d-4b49-9d01-759849e377e1 · outbound

This paper cites PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs.

BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:49.411540Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation b5f1c749-22c9-4e33-9678-f6d57249a76e · inbound

PINNs Failure Modes are Overfitting cites this paper.

PINNs Failure Modes are Overfitting BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-06-29T00:02:49.918375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.