Pith. sign in

Paper Citation Record · LEDGER

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation

As of 18 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2506.01976.

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

pith.paper-citation-record.v1
2506.01976 v2

Coverage vector

measured 57 of 57 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T21:08:50.521949Z

measured 57 of 57 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

57 of 57 outbound references displayed

  • verified exact1
  • verified fuzzy42
  • unresolved14
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b94d87ff-581f-4e7b-a8ef-e2cad56dc6ce · outbound

This paper cites The dynamics of rapid fracture: insta- bilities, nonlinearities and length scales.Reports on Progress in Physics, 77(4):046501, 2014.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation The dynamics of rapid fracture: insta- bilities, nonlinearities and length scales.Reports on Progress in Physics, 77(4):046501, 2014

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.168303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.323442Z digest=sha256:6916937f7b388eb37b5b6ca85743d265c8b3de951edc3d414870e8e7a80697af

Observation cdd1e477-4633-455c-84b4-9e0a18c73ee2 · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:53.150887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.352043Z digest=sha256:a3c4641cb49db21fb4b77453b8b9262343a3a67d1b7cf6e73ddb08f98ace7182

Observation e6696a41-4729-4170-a223-0490b462660b · outbound

This paper cites Elastic crack growth in finite elements with minimal remesh- ing.International journal for numerical methods in engineering, 45(5):601–620, 1999.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Elastic crack growth in finite elements with minimal remesh- ing.International journal for numerical methods in engineering, 45(5):601–620, 1999

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.132782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.358448Z digest=sha256:5e608587391f2cdde8559603434332d832f89f739f6750cb64d42dd475be061d

Observation 7fbc7489-def5-4e09-9d45-fc5831913446 · outbound

This paper cites The fracture mechanics of finite crack exten- sion.Engineering Fracture Mechanics, 72(7):1021–1038, 2005.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation The fracture mechanics of finite crack exten- sion.Engineering Fracture Mechanics, 72(7):1021–1038, 2005

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.113337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.409774Z digest=sha256:2700aca04b854e54aecb68fb111a87c49f9eda28fdb2115864163b72f7ea3b70

Observation 558e34f4-1714-4e84-81e2-08141b98c797 · outbound

This paper cites A finite element method for localized failure analysis.Computer methods in applied mechanics and engineering, 61(2):189–214, 1987.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A finite element method for localized failure analysis.Computer methods in applied mechanics and engineering, 61(2):189–214, 1987

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.096913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.434736Z digest=sha256:bff538ec18f4e8778a3eb9950cf1808ea9ab37d911c370eed16dd25b6053c4b7

Observation b4de106a-e031-450c-9ca2-d1c4a987c36f · outbound

This paper cites Yielding of steel sheets containing slits.Journal of the Mechanics and Physics of Solids, 8(2):100–104, 1960.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Yielding of steel sheets containing slits.Journal of the Mechanics and Physics of Solids, 8(2):100–104, 1960

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.080633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.441180Z digest=sha256:31a663b7425d6b8ccc46e3fb8d0801d731275bcf3045c8c7be82cb0bb9addcbd

Observation 760c4dff-fe43-4dae-8096-afe2e7ad29da · outbound

This paper cites A comparative review of peridynamics and phase-field models for engineering fracture mechanics.Computational Me- chanics, 69(6):1259–1293, 2022.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A comparative review of peridynamics and phase-field models for engineering fracture mechanics.Computational Me- chanics, 69(6):1259–1293, 2022

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.063200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.447586Z digest=sha256:83f9fdc7f81b067b51fc5d73b93495a6d3a58f5b3eb6a9fce315c52b5576c085

Observation 8e3b3175-edac-4aa7-ab87-99f4ab70d1f5 · outbound

This paper cites Phase-field models in materials science.Modelling and simulation in materials science and engineering, 17(7):073001, 2009.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Phase-field models in materials science.Modelling and simulation in materials science and engineering, 17(7):073001, 2009

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.046842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.490127Z digest=sha256:63af89fc3c1de29323bf6cf9cd835c4750103b5b052736d375bea530d4abb7bb

Observation 1232e75b-e04b-45b3-a0fe-d02ab0a67cba · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:53.029584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.509723Z digest=sha256:8a771ee59df3f56ea2d0e2b27c4f0710b6452537f4e4c88e06aa8c3103b920ec

Observation 549631df-70e2-4d33-a781-f8493dab365e · outbound

This paper cites An introduction to phase-field modeling of microstructure evolution.Calphad, 32(2):268–294, 2008.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation An introduction to phase-field modeling of microstructure evolution.Calphad, 32(2):268–294, 2008

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:53.010966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.515743Z digest=sha256:c1f2618a84b9142d1066d416ea645949468474cb4df4d125e8b5bea60e9dc5e9

Observation 4240820f-6564-48b5-a5ee-32d80c0bc1b5 · outbound

This paper cites Phase-field modeling of fracture.Advances in applied mechanics, 53:1– 183, 2020.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Phase-field modeling of fracture.Advances in applied mechanics, 53:1– 183, 2020

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.991806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.526762Z digest=sha256:3c093f650d6b35c53a4d02d35f2e5a2b1c3f4f45b5c490525636c4d7fe179eb3

Observation 49839fd7-2899-4078-9b7c-91690a2564d0 · outbound

This paper cites Machine- learning-based data-driven discovery of nonlinear phase-field dynamics.Physical Review E, 106(6):065303, 2022.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Machine- learning-based data-driven discovery of nonlinear phase-field dynamics.Physical Review E, 106(6):065303, 2022

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.974478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.554152Z digest=sha256:43b127573f4d2758ae379dc6a19c5a9133fc313d4389a272d411a7e73fa41107

Observation 0ad7cab4-2bd2-408c-9c5a-4d5d9477348b · outbound

This paper cites A phase field modeling approach of cyclic fatigue crack growth.International Journal of Fracture, 225(1):89–100, 2020.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A phase field modeling approach of cyclic fatigue crack growth.International Journal of Fracture, 225(1):89–100, 2020

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.957882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.629329Z digest=sha256:eb59601b3ee90aff9595469799afcd15a5d4317448e75cf3f0b8668f3e9793b1

Observation 33af7f8d-c5fd-4d03-b74c-ebf5d9810de2 · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:52.940736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.670597Z digest=sha256:460a9190dadf145e02584fe584d1aaa37b85364cb6ed99764ba66cbc578f6e31

Observation 9cb9c8ca-2884-4d11-aaa9-9aa7e9d8b25a · outbound

This paper cites Numerical implementation of phase-field models of brittle fracture.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Numerical implementation of phase-field models of brittle fracture

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.921241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.675612Z digest=sha256:6b7c2084bfdb7139a5ee11a0b76cf725e877cfcbcbceae3c536b3c607de23d19

Observation 1d8f1a88-a3ef-44eb-8229-fcd8232d93ac · outbound

This paper cites Numerical experiments in revis- ited brittle fracture.Journal of the Mechanics and Physics of Solids, pages 797–826, 2000.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Numerical experiments in revis- ited brittle fracture.Journal of the Mechanics and Physics of Solids, pages 797–826, 2000

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.901195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.681559Z digest=sha256:5c77afd37c0705b594b426bda9b4e5dc3eac623a30b89d54a7fcb5339607539e

Observation 54dde977-8862-426e-bb53-fe3085fa717f · outbound

This paper cites Francfort, and Jean-Jacques Marigo.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Francfort, and Jean-Jacques Marigo

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.883175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.719135Z digest=sha256:94f6295e8e895f5c35a9a60f65d7216a4a74a929cb362372f9b05ca22823657e

Observation 38d3a8f7-2342-4d3e-9371-829a0348e0f4 · outbound

This paper cites Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow.Computer Methods in Applied Mechanics and Engineering, 330:1–32, 2018.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow.Computer Methods in Applied Mechanics and Engineering, 330:1–32, 2018

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.865317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.780954Z digest=sha256:59e2aafb55a53895227f139b7527780b07a9758e22023d67824ddf4099c4321e

Observation 486a161e-1d75-4b79-93e0-61b8435db1c9 · outbound

This paper cites A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.848518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.788623Z digest=sha256:e99de309a59e368d5dcb1dfe8919d5f4faf7ebc2975da9e46ffff27e9d092d1e

Observation ca2ebedd-fef4-416c-8720-0fa9954b2d38 · outbound

This paper cites A lattice-based model of the kinetics of twin boundary motion.Journal of the Mechanics and Physics of Solids, 51(9):1675–1700, 2003.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A lattice-based model of the kinetics of twin boundary motion.Journal of the Mechanics and Physics of Solids, 51(9):1675–1700, 2003

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-15T21:08:49.794196Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T21:08:49.794196Z digest=sha256:5975b4b5056be49ff600af5aabb888096cf9475db0eecd47c8e894ce25cbfbee

Observation 40db0a11-38b0-4bb4-9baa-964d9d159c29 · outbound

This paper cites Multiresolution atomistic simulations of dynamic fracture in nanostructured ce- ramics and glasses.International Journal of Fracture, 121:71–79, 2003.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Multiresolution atomistic simulations of dynamic fracture in nanostructured ce- ramics and glasses.International Journal of Fracture, 121:71–79, 2003

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.823083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.825298Z digest=sha256:55cd9bfe05498f174817bd3217d1a861aef0b774e557ec2be13858067e84acfd

Observation f20a0b92-1ac9-4405-9c86-3c5a902a82d1 · outbound

This paper cites Constitutively informed multi-body interactions for lattice particle models.Computer Methods in Applied Mechanics and Engineering, 366:113052, 2020.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Constitutively informed multi-body interactions for lattice particle models.Computer Methods in Applied Mechanics and Engineering, 366:113052, 2020

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.806679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.862471Z digest=sha256:f85081a4f1ce439d60e4fc7c43c3e417aab1c9c705da540fdc3a4c4dcd511dd9

Observation e30d04a3-60c0-40fc-a94d-cfa310395fcb · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:52.791835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.871175Z digest=sha256:f63ec9832696dbdbd6611f27541ab6eef8a5e39c9a5903e64fb914cf50e60734

Observation 6de4fa0e-47fd-4109-a7c3-ea81b92fd56b · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:52.776892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.876041Z digest=sha256:41818e94fc022fbe37135c129e95079da4d4ddfff6d7b686e3b5debed211bdcc

Observation 9182cc99-9735-43be-a0e0-728383115519 · outbound

This paper cites Modeling failure of hyperelastic solids inter- acting with fluids.Computational Particle Mechanics, 12(1):153–164, 2025.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Modeling failure of hyperelastic solids inter- acting with fluids.Computational Particle Mechanics, 12(1):153–164, 2025

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.761460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.881450Z digest=sha256:63181e699f31af0651b8147f88e65c5d7698873593a897df16c6913efaf63e45

Observation 521fb615-17f9-42c9-a984-46c75c95efae · outbound

This paper cites Modeling the role of phase boundaries on the pullout response of shape memory wire reinforced composites.Mechanics of Advanced Materials and Structures, 30(6):1128–1137, 2023.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Modeling the role of phase boundaries on the pullout response of shape memory wire reinforced composites.Mechanics of Advanced Materials and Structures, 30(6):1128–1137, 2023

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.743757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.916684Z digest=sha256:48ee0a7d66ddef362603a0b9c6a8bb98b864fcfcbc6434e10001733d54765c67

Observation 7730c684-4587-46d7-9242-f098805eb67d · outbound

This paper cites Fuhg, G.A.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Fuhg, G.A

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.726274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.943031Z digest=sha256:9d28ade45033b70c204b498c2d364f255dfb908c19a83b008b588622ef400221

Observation a76079d7-5c14-4ec9-a14f-85fa2bda2443 · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:52.709853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.948302Z digest=sha256:a6390168db3aa81cc03b1076f921eb1269bd5444773c759ed521f8c1960961fd

Observation b875474f-ec09-46d8-be4d-c7c82fa5b9af · outbound

This paper cites Phase-field modeling of fracture with physics-informed deep learning.Computer Methods in Applied Me- chanics and Engineering, page 117104, 2024.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Phase-field modeling of fracture with physics-informed deep learning.Computer Methods in Applied Me- chanics and Engineering, page 117104, 2024

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.671567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:49.953207Z digest=sha256:f1db7d12b94d92fb02ee0a18b6f28986ba704c2b5605f3d56c3063a90d10870b

Observation 846e5961-81a7-4c7b-a86f-68dff097a291 · outbound

This paper cites Predicting crack nucleation and propagation in brittle materials using deep operator networks with diverse trunk architectures.arXiv preprint arXiv:2501.00016, 2024.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Predicting crack nucleation and propagation in brittle materials using deep operator networks with diverse trunk architectures.arXiv preprint arXiv:2501.00016, 2024

Reference 30

Resolution
verified exact
raw_fallback, observed 2026-08-15T21:08:50.810027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.016737Z digest=sha256:a9d405f508a267f5d88e63fabf6a2924e1def5e73d8c97459cf7ee27710e45aa

Observation 02acf3e8-0093-48a8-a402-54854d87a5ad · outbound

This paper cites Transfer learning enhanced physics informed neural network for phase-field modeling of fracture.The- oretical and Applied Fracture Mechanics, 106:102447, 2020.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Transfer learning enhanced physics informed neural network for phase-field modeling of fracture.The- oretical and Applied Fracture Mechanics, 106:102447, 2020

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.637710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.022387Z digest=sha256:b0fff7b2f680cf6b0334bc550ac2b3193b6966c5b497d2493a632f608c8cc57e

Observation bb8a2549-bd8e-4159-a79e-4aa45f282612 · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:52.552076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.027760Z digest=sha256:9f464f94ee99e06c79083738d1054c2532ed5913f1b4977952feb4b27d83f1dc

Observation de1bc406-027c-4d84-9016-5f6bd06c16bd · outbound

This paper cites Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks.International Journal of Fatigue, 186:108382, 2024.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks.International Journal of Fatigue, 186:108382, 2024

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.433682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.068328Z digest=sha256:21240f5046b1292eed17839cec690d7df4efe70b66330009dd660cd89fcbee7f

Observation 703e2efc-06a0-4881-9325-047d2f9229e5 · outbound

This paper cites Ma- chine learning accelerated discrete element modeling of granular flows.Chemical Engineering Science, 245:116832, 2021.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Ma- chine learning accelerated discrete element modeling of granular flows.Chemical Engineering Science, 245:116832, 2021

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.416600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.089441Z digest=sha256:1d487bb0705685b2cb1e27fbb7afd09f4d21bbf82ef16ff54400c14e9a903322

Observation 2fa4d779-df52-49a7-a303-3d0e8265c43f · outbound

This paper cites Advances in the characterization of residual stress in composite structures.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Advances in the characterization of residual stress in composite structures

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.372293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.095155Z digest=sha256:02184e430d43cc27ac89a605576db788d3aa19f39da36c675b26543556341d4d

Observation eb8102ce-86d5-4fb0-a3ac-dd924b7281c4 · outbound

This paper cites A discrete element solution method em- bedded within a neural network.Powder Technology, 448:120258, 2024.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A discrete element solution method em- bedded within a neural network.Powder Technology, 448:120258, 2024

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.314655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.100340Z digest=sha256:fb0be918d1abf2302688c2f954a5e9abf0db6366590aa082de5661993bf89892

Observation 71859863-ecaf-4525-8974-86d07a61c4f5 · outbound

This paper cites A novel ml-dem algorithm for predicting particle motion in rotary drums.Engi- neering Analysis with Boundary Elements, 177:106258, 2025.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A novel ml-dem algorithm for predicting particle motion in rotary drums.Engi- neering Analysis with Boundary Elements, 177:106258, 2025

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.196539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.144967Z digest=sha256:9b9cd17125106530a87d98c06e5e1f4b3616547533fc4fc56262647e769a32ac

Observation f9b5b380-d685-4de9-b120-cf1e03ad39b3 · outbound

This paper cites Karniadakis.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Karniadakis

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.134732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.186382Z digest=sha256:d3038776f4f00d9c4c889afde13c4aa8e213bb31578ba3fb6b24b9425c362ace

Observation 700459f5-8823-4572-a132-9c34ebc84aa4 · outbound

This paper cites Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural opera- tor learning.International Journal of Multiphase Flow, 180:104959, 2024.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural opera- tor learning.International Journal of Multiphase Flow, 180:104959, 2024

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:52.016140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.192135Z digest=sha256:4260fe25c3f1faa46c43e8c38c22dfdc23263373159cf0f245fae32ffe446aa3

Observation ea9ace80-a7ba-4820-b027-eb9f3804d807 · outbound

This paper cites Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity

Reference 40

Resolution
unresolved
no resolver link, observed 2026-08-15T21:08:50.198621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T21:08:50.198621Z digest=sha256:8ccdda1e4fe509800b3c43f117fca297548c90c44d7c87a169c6f592715fd479

Observation 839df78f-be3e-436c-963f-500ecbf40fad · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, pages 1–97, 2023.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, pages 1–97, 2023

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.908023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.233210Z digest=sha256:b202967f7f736eed43d455c9c05fb68d4e81c713688b0d41e095267100f33f9d

Observation c19523d9-caf2-46c3-9178-044867e3e5d4 · outbound

This paper cites A causality-deeponet for causal responses of linear dynamical systems.Communications in Computational Physics, pages 1194–1228, 2024.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation A causality-deeponet for causal responses of linear dynamical systems.Communications in Computational Physics, pages 1194–1228, 2024

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.890412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.239258Z digest=sha256:49d086ad67c69ba863af45f25f70444976b4531792ab48da0ca204ab855fac88

Observation d7d805f0-dd55-4391-b787-59a83f7b790d · outbound

This paper cites Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-15T21:08:50.244734Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T21:08:50.244734Z digest=sha256:5909ed5158d8cd3aad0f4b9fb1a13a644a5fc0567132cacb1883da30c8bfa2dd

Observation 9a34a808-e5fc-4c95-aef5-1e3fa609a138 · outbound

This paper cites Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flows.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flows

Reference 44

Resolution
unresolved
no resolver link, observed 2026-08-15T21:08:50.278007Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T21:08:50.278007Z digest=sha256:25187cadb2c221263b6e1989f2d98a2322325c86e4dedd42e2d4112ef65ee50b

Observation ae59a472-6b2b-4c0c-8f9e-0fbc66bd6746 · outbound

This paper cites Learning the solution operator of para- metric partial differential equations with physics-informed deeponets.Science Advances, page eabi8605, 2021.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Learning the solution operator of para- metric partial differential equations with physics-informed deeponets.Science Advances, page eabi8605, 2021

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.833880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.307586Z digest=sha256:cc963d8ee3cc8d7c8f4ff2e2b1d842b6736e50b5d735978df3074a4585206c69

Observation 77c8317b-da46-4e8e-9a6d-04c348fe9ea9 · outbound

This paper cites On the training and generalization of deep operator net- works.SIAM Journal on Scientific Computing, pages C273–C296, 2024.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation On the training and generalization of deep operator net- works.SIAM Journal on Scientific Computing, pages C273–C296, 2024

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.658368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.327705Z digest=sha256:5e8b76bbae8b570ed89b42a10612f3b00a12aefde5f09ba870203ef9cf12b6e0

Observation 89b70807-420f-43f9-8ba7-16ef198ef6dd · outbound

This paper cites Jagtap, and George E.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Jagtap, and George E

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.557669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.360752Z digest=sha256:f704eb2a621902c4f58c27b44706aea061038b81420ac94bb73b2242aa77146a

Observation 3e6f5867-f281-4017-9a25-42b3c422d07d · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation KAN: Kolmogorov-Arnold Networks

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-15T21:08:50.376864Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T21:08:50.376864Z digest=sha256:99adf178ef31f2e5576d61eb85d84146ede65da45f404acf4355d60bcb5da0b0

Observation 812d7e11-92d7-4c56-b490-8d383af63f8f · outbound

This paper cites Sprecher and Sorin Draghici.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Sprecher and Sorin Draghici

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.539798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.383074Z digest=sha256:4d9a124433f3b33f504edcd3574fd86af7a74dae6b1b16d1ef28167138049c5a

Observation 8c9e9b4d-d142-47b4-9b83-c37a6d657173 · outbound

This paper cites On the training of a kolmogorov network.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation On the training of a kolmogorov network

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.297063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.387558Z digest=sha256:7c44f220cf2182444fedb9948bfe7dedd11f33c424f7c9e289842016b59d733d

Observation f11a28b8-5b62-4215-a538-17918d28a91f · outbound

This paper cites Crack-net: A deep learning approach to predict crack propagation and stress–strain curves in particulate composites.Engineering, 2025.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Crack-net: A deep learning approach to predict crack propagation and stress–strain curves in particulate composites.Engineering, 2025

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.196087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.434653Z digest=sha256:6048491800f1a170abf6440047c714237b3c41e019860423a3c23226b3668440

Observation db725c95-0f52-4acd-80ab-f24d209b1bf0 · outbound

This paper cites Modelling de- lamination of elastic layers from shape memory alloy substrates.Shape Memory and Superelas- ticity, pages 1–10, 2025.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Modelling de- lamination of elastic layers from shape memory alloy substrates.Shape Memory and Superelas- ticity, pages 1–10, 2025

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:51.077579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.439764Z digest=sha256:e7a76cd9efd2c437947f41ce9cc156de4022dbecbcf78b90d887fee9b22fa283

Observation b0289919-5429-4cbc-b856-5338610ffce4 · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:51.058821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.444306Z digest=sha256:f2e382b53c5697a1dc5663480cdc909a1c98665f73acd82080cbaa792bca17f6

Observation e6e32c8a-4c83-468c-973e-bd4a018962b7 · outbound

This paper cites an unresolved cited work.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-08-15T21:08:51.006682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.449949Z digest=sha256:cb86e916b60e29c0d7bd17a48414d392bdcd1dd01b920d254291e6716f0197f4

Observation dabb0a49-0e3d-4691-b83c-574b337aa338 · outbound

This paper cites An abaqus implementation of the ex- tended finite element method.Engineering fracture mechanics, 76(3):347–368, 2009.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation An abaqus implementation of the ex- tended finite element method.Engineering fracture mechanics, 76(3):347–368, 2009

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:50.988009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.491025Z digest=sha256:ca420dfe8f793cd54159e7292e2ebac5e905df6cfe9618f62ee760e7544fac1b

Observation 65bfe6c6-9cbe-422e-97ca-91be3f474bd8 · outbound

This paper cites Mechanics of the crack path formation.International Journal of Fracture, 47:291–305, 1991.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Mechanics of the crack path formation.International Journal of Fracture, 47:291–305, 1991

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:50.902710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.516156Z digest=sha256:597c1d8c70cd32131f58dda6f82a47096e369a9e8995c027d690c393f05171e6

Observation b4f9a4c6-7e99-4162-adc6-73135de26fee · outbound

This paper cites Deep Kro- necker neural networks: A general framework for neural networks with adaptive activation functions.Neurocomputing, 468:165–180, 2022.

Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Deep Kro- necker neural networks: A general framework for neural networks with adaptive activation functions.Neurocomputing, 468:165–180, 2022

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T21:08:50.867788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T21:08:50.521949Z digest=sha256:b59d50742364dddf973f749c90cd8f2935eda4b3c2bced8aea02363566875188

Pith citing papers

No inbound Pith citation observations are available.