Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T21:08:50.521949Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T21:08:50.521949Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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
57 of 57 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation b94d87ff-581f-4e7b-a8ef-e2cad56dc6ce · outbound
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
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.
Observation cdd1e477-4633-455c-84b4-9e0a18c73ee2 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 2
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.
Observation e6696a41-4729-4170-a223-0490b462660b · outbound
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
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.
Observation 7fbc7489-def5-4e09-9d45-fc5831913446 · outbound
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
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.
Observation 558e34f4-1714-4e84-81e2-08141b98c797 · outbound
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
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.
Observation b4de106a-e031-450c-9ca2-d1c4a987c36f · outbound
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
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.
Observation 760c4dff-fe43-4dae-8096-afe2e7ad29da · outbound
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
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.
Observation 8e3b3175-edac-4aa7-ab87-99f4ab70d1f5 · outbound
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
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.
Observation 1232e75b-e04b-45b3-a0fe-d02ab0a67cba · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 9
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.
Observation 549631df-70e2-4d33-a781-f8493dab365e · outbound
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
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.
Observation 4240820f-6564-48b5-a5ee-32d80c0bc1b5 · outbound
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
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.
Observation 49839fd7-2899-4078-9b7c-91690a2564d0 · outbound
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
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.
Observation 0ad7cab4-2bd2-408c-9c5a-4d5d9477348b · outbound
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
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.
Observation 33af7f8d-c5fd-4d03-b74c-ebf5d9810de2 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 14
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.
Observation 9cb9c8ca-2884-4d11-aaa9-9aa7e9d8b25a · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Numerical implementation of phase-field models of brittle fracture
Reference 15
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.
Observation 1d8f1a88-a3ef-44eb-8229-fcd8232d93ac · outbound
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
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.
Observation 54dde977-8862-426e-bb53-fe3085fa717f · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Francfort, and Jean-Jacques Marigo
Reference 17
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.
Observation 38d3a8f7-2342-4d3e-9371-829a0348e0f4 · outbound
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
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.
Observation 486a161e-1d75-4b79-93e0-61b8435db1c9 · outbound
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
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.
Observation ca2ebedd-fef4-416c-8720-0fa9954b2d38 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 40db0a11-38b0-4bb4-9baa-964d9d159c29 · outbound
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
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.
Observation f20a0b92-1ac9-4405-9c86-3c5a902a82d1 · outbound
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
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.
Observation e30d04a3-60c0-40fc-a94d-cfa310395fcb · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 23
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.
Observation 6de4fa0e-47fd-4109-a7c3-ea81b92fd56b · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 24
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.
Observation 9182cc99-9735-43be-a0e0-728383115519 · outbound
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
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.
Observation 521fb615-17f9-42c9-a984-46c75c95efae · outbound
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
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.
Observation 7730c684-4587-46d7-9242-f098805eb67d · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Fuhg, G.A
Reference 27
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.
Observation a76079d7-5c14-4ec9-a14f-85fa2bda2443 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 28
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.
Observation b875474f-ec09-46d8-be4d-c7c82fa5b9af · outbound
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
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.
Observation 846e5961-81a7-4c7b-a86f-68dff097a291 · outbound
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
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.
Observation 02acf3e8-0093-48a8-a402-54854d87a5ad · outbound
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
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.
Observation bb8a2549-bd8e-4159-a79e-4aa45f282612 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 32
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.
Observation de1bc406-027c-4d84-9016-5f6bd06c16bd · outbound
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
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.
Observation 703e2efc-06a0-4881-9325-047d2f9229e5 · outbound
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
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.
Observation 2fa4d779-df52-49a7-a303-3d0e8265c43f · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Advances in the characterization of residual stress in composite structures
Reference 35
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.
Observation eb8102ce-86d5-4fb0-a3ac-dd924b7281c4 · outbound
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
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.
Observation 71859863-ecaf-4525-8974-86d07a61c4f5 · outbound
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
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.
Observation f9b5b380-d685-4de9-b120-cf1e03ad39b3 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Karniadakis
Reference 38
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.
Observation 700459f5-8823-4572-a132-9c34ebc84aa4 · outbound
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
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.
Observation ea9ace80-a7ba-4820-b027-eb9f3804d807 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 839df78f-be3e-436c-963f-500ecbf40fad · outbound
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
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.
Observation c19523d9-caf2-46c3-9178-044867e3e5d4 · outbound
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
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.
Observation d7d805f0-dd55-4391-b787-59a83f7b790d · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9a34a808-e5fc-4c95-aef5-1e3fa609a138 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae59a472-6b2b-4c0c-8f9e-0fbc66bd6746 · outbound
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
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.
Observation 77c8317b-da46-4e8e-9a6d-04c348fe9ea9 · outbound
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
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.
Observation 89b70807-420f-43f9-8ba7-16ef198ef6dd · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Jagtap, and George E
Reference 47
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.
Observation 3e6f5867-f281-4017-9a25-42b3c422d07d · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation KAN: Kolmogorov-Arnold Networks
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 812d7e11-92d7-4c56-b490-8d383af63f8f · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Sprecher and Sorin Draghici
Reference 49
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.
Observation 8c9e9b4d-d142-47b4-9b83-c37a6d657173 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation On the training of a kolmogorov network
Reference 50
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.
Observation f11a28b8-5b62-4215-a538-17918d28a91f · outbound
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
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.
Observation db725c95-0f52-4acd-80ab-f24d209b1bf0 · outbound
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
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.
Observation b0289919-5429-4cbc-b856-5338610ffce4 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 53
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.
Observation e6e32c8a-4c83-468c-973e-bd4a018962b7 · outbound
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation Unresolved cited work
Reference 54
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.
Observation dabb0a49-0e3d-4691-b83c-574b337aa338 · outbound
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
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.
Observation 65bfe6c6-9cbe-422e-97ca-91be3f474bd8 · outbound
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
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.
Observation b4f9a4c6-7e99-4162-adc6-73135de26fee · outbound
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
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.
No inbound Pith citation observations are available.