Paper Citation Record · LEDGER

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials

As of 19 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2506.16918.

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

pith.paper-citation-record.v1
2506.16918 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T23:41:59.783436Z

measured 31 of 31 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

31 of 31 outbound references displayed

verified exact6
verified fuzzy5
unresolved11
parse uncertain0
malformed identifier5
metadata mismatch4

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e98a8ea4-f7d6-4b83-a7da-026fcaebbac9 · outbound

This paper cites Model Reduction and Neural Networks for Parametric PDEs.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Model Reduction and Neural Networks for Parametric PDEs

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.319173Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b652bb8-d266-4f53-b45c-fd963136ab8c · outbound

This paper cites Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems

Reference 2

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T23:42:01.066600Z

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 c237a9c2-9b91-4943-937b-3cf542847c3c · outbound

This paper cites FE-LSTM: A hybrid approach to accelerate multiscale simulations of architectured materials using Recurrent Neural Networks and Finite Element Analysis.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials FE-LSTM: A hybrid approach to accelerate multiscale simulations of architectured materials using Recurrent Neural Networks and Finite Element Analysis

Reference 3

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T23:42:00.829655Z

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 55e1d0f3-b56d-4700-a24d-bc066790ef4c · outbound

This paper cites FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Gener- ation, and Implementation.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Gener- ation, and Implementation

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:42:01.044510Z

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 3a466459-6393-40c3-82bf-ba8ae6f8ef5f · outbound

This paper cites Nonlinear model reduction for operator learning.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Nonlinear model reduction for operator learning

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.374750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4dffe55-9cc1-4777-b26d-3da710224b07 · outbound

This paper cites Equino: A physics-informed neural operator for multiscale simulations.arXiv preprint arXiv:2504.07976, 2025.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Equino: A physics-informed neural operator for multiscale simulations.arXiv preprint arXiv:2504.07976, 2025

Reference 6

Resolution: verified exact; doi, observed 2026-08-06T23:42:00.060225Z

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 0576bc86-79cc-44d8-859a-632879b258d0 · outbound

This paper cites Multiscale FE2 elastoviscoplastic analysis of composite structures.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Multiscale FE2 elastoviscoplastic analysis of composite structures

Reference 7

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T23:42:01.024371Z

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 a08d0438-b600-4751-8736-e89ce3c7df23 · outbound

This paper cites A remark on the application of the Newton-Raphson method in non- linear finite element analysis.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials A remark on the application of the Newton-Raphson method in non- linear finite element analysis

Reference 8

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T23:42:01.000866Z

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 447438a6-3777-4d66-898d-ce46cc419492 · outbound

This paper cites an unresolved cited work.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.435814Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d20485f7-fa03-4ea4-bcdf-e43e4c3e51c4 · outbound

This paper cites Physics informed neural networks for continuum micromechanics.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Physics informed neural networks for continuum micromechanics

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.442128Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0abd90cc-10ac-4a28-a704-d445e784e24f · outbound

This paper cites Generalizing universal function approximators.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Generalizing universal function approximators

Reference 11

Resolution: verified exact; doi, observed 2026-08-06T23:41:59.929925Z

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 ba66c54d-8605-4fbe-8550-5bc6e3589fe9 · outbound

This paper cites Kochmann, Jonathan B.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Kochmann, Jonathan B

Reference 12

Resolution: verified exact; doi, observed 2026-08-06T23:41:59.914145Z

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 77b1ff58-04c6-48ad-b43d-00420496923b · outbound

This paper cites On universal approximation and error bounds for Fourier Neural Operators.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials On universal approximation and error bounds for Fourier Neural Operators

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.534285Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf20bcda-3964-4556-9cff-e920c73d6070 · outbound

This paper cites Combining Physics-based and Data-driven Modeling for Building Energy Systems.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Combining Physics-based and Data-driven Modeling for Building Energy Systems

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:42:00.965687Z

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 a025683e-9411-4fb4-ab6a-bad5e4fbd243 · outbound

This paper cites In vitro and in vivo study of additive manufactured porous Ti6Al4V scaffolds for repairing bone defects.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials In vitro and in vivo study of additive manufactured porous Ti6Al4V scaffolds for repairing bone defects

Reference 15

Resolution: verified exact; doi, observed 2026-08-06T23:41:59.897639Z

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 0b3f3a4f-d4b3-46c5-9e73-99fc1656dbb2 · outbound

This paper cites DeepONet: Learning nonlinear oper- ators for identifying differential equations based on the universal approximation theorem of operators, October 2019.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials DeepONet: Learning nonlinear oper- ators for identifying differential equations based on the universal approximation theorem of operators, October 2019

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:42:00.947973Z

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 7d0b3cae-e46a-4aa5-9314-f9a1c7bb5e73 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 17

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T23:42:00.930567Z

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 b2c5df57-0a34-4c01-b368-2a50168c33fb · outbound

This paper cites A comprehensive and fair comparison of two neural operators (with practical extensions) based on F AIR data.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials A comprehensive and fair comparison of two neural operators (with practical extensions) based on F AIR data

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.640162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7005b4fe-f059-426e-8141-97ae221d1b87 · outbound

This paper cites an unresolved cited work.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.646431Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37cb99ae-1749-4502-95c8-87c829d8f080 · outbound

This paper cites Patel, Nathaniel A.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Patel, Nathaniel A

Reference 20

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T23:42:00.358295Z

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 00b3f89c-84e3-46cc-b4e4-9ef3d36d3be2 · outbound

This paper cites an unresolved cited work.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:42:00.913576Z

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 6426d74c-2745-4495-a494-07865c49372c · outbound

This paper cites Rokoˇ s, R.H.J.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Rokoˇ s, R.H.J

Reference 22

Resolution: malformed identifier; no resolver link, observed 2026-08-06T23:41:59.733269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5597fefd-d2c8-4403-81b2-160ebbb05b1c · outbound

This paper cites Kalina, J¨ org Brummund, and Markus K¨ astner.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Kalina, J¨ org Brummund, and Markus K¨ astner

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.747184Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e20403e-f207-4474-8a54-4a23cb03ad06 · outbound

This paper cites Kalina, J¨ org Brummund, WaiChing Sun, and Markus K¨ astner.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Kalina, J¨ org Brummund, WaiChing Sun, and Markus K¨ astner

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.755333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6d9a66b-ec36-4243-96b6-e565d841e070 · outbound

This paper cites Staub, H.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Staub, H

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:42:00.891593Z

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 621989cd-c102-4e0d-8149-bb41e986c860 · outbound

This paper cites Tikarrouchine, G.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Tikarrouchine, G

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:42:00.875628Z

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 6f3ed214-1258-4536-80ab-58891f37cc98 · outbound

This paper cites Iterated learning and multiscale modeling of history-dependent architectured metamaterials.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Iterated learning and multiscale modeling of history-dependent architectured metamaterials

Reference 27

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T23:42:00.197178Z

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 68d66eb0-f7ba-41ac-a411-2b2acba1aeda · outbound

This paper cites doi: 10.1016/j.ijsolstr.2019.01.018.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials doi: 10.1016/j.ijsolstr.2019.01.018

Reference 2019

Resolution: verified exact; doi, observed 2026-08-06T23:41:59.834240Z

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 63a691bc-1dc4-4734-bbc5-349d6a22b308 · outbound

This paper cites an unresolved cited work.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Unresolved cited work

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-06T23:41:59.724662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e30521b-e2de-41c9-800c-d1e6f7db09ef · outbound

This paper cites doi: 10.3390/mca28040091.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials doi: 10.3390/mca28040091

Reference 2023

Resolution: verified exact; doi, observed 2026-08-06T23:42:00.109603Z

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 8f3cc783-8c3c-4c06-b75e-02c08071770c · outbound

This paper cites doi: 10.1016/j.apenergy.2025.125853.

A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials doi: 10.1016/j.apenergy.2025.125853

Reference 2025

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T23:42:00.624958Z

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.

Pith citing papers

No inbound Pith citation observations are available.