Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks | Paper Citation Record

Observation 465f0bd0-8a0b-409e-8e62-882112f61ba9 · outbound

This paper cites Physics Informed Neural Net- works for Modeling of 3D Flow-Thermal Problems with Sparse Domain Data.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Physics Informed Neural Net- works for Modeling of 3D Flow-Thermal Problems with Sparse Domain Data

Reference 1

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T17:10:55.737783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 45e4c3c9-bb58-4069-b7d9-0bfe4d871c8c · outbound

This paper cites Hemo- dynamics modeling with physics-informed neural networks: A progressive boundary complexity approach.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Hemo- dynamics modeling with physics-informed neural networks: A progressive boundary complexity approach

Reference 2

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T17:10:56.714746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b6fa65ed-03da-40cd-9b92-6aed19e05447 · outbound

This paper cites Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:59.206001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 673ac132-1aad-47be-b0ef-1a4e588bdcac · outbound

This paper cites Eulerian formulation of the tensor-based morphology equations for strain-based blood damage modeling.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Eulerian formulation of the tensor-based morphology equations for strain-based blood damage modeling

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:49.779041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bdcd837f-1f25-4b64-9b90-e651f0082f13 · outbound

This paper cites Application of CFD to Analyze the Hydrodynamic Behaviour of a Biore- actor with a Double Impeller.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Application of CFD to Analyze the Hydrodynamic Behaviour of a Biore- actor with a Double Impeller

Reference 5

Resolution: verified exact; doi, observed 2026-08-06T17:10:55.552817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 663d6f0c-0920-48ee-97fd-787d76bb212a · outbound

This paper cites Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:49.980592Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac9c5f9b-4602-4b7b-a0e0-b044d67d9021 · outbound

This paper cites Faroughi, Nikhil M.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Faroughi, Nikhil M

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:50.094037Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69eca43d-9995-483e-947d-d669299fdd55 · outbound

This paper cites Garcia-Ochoa, V.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Garcia-Ochoa, V

Reference 8

Resolution: verified exact; doi, observed 2026-08-06T17:10:55.384082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b702de83-5227-45c1-b9e2-ae21f4a5d6ac · outbound

This paper cites Geometry-aware PINNs for Turbulent Flow Prediction, December 2024.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Geometry-aware PINNs for Turbulent Flow Prediction, December 2024

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:59.000154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 76a2f83a-769b-4b74-bb71-6942cdd555e3 · outbound

This paper cites A physics- informed deep learning framework for inversion and surrogate modeling in solid mechanics.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks A physics- informed deep learning framework for inversion and surrogate modeling in solid mechanics

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:50.458136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78fec7a0-6fda-4d8c-9caf-8859ac4cb44f · outbound

This paper cites an unresolved cited work.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Unresolved cited work

Reference 11

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T17:10:55.182743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f2ddd20f-02f4-415f-b627-ec784ed92d6a · outbound

This paper cites Flow field reconstruction from sparse sensor mea- surements with physics-informed neural networks.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Flow field reconstruction from sparse sensor mea- surements with physics-informed neural networks

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:50.665472Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e86eb365-f772-40cd-a708-fff0b4a8452f · outbound

This paper cites A General Review of the Current Development of Mechanically Agitated Vessels.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks A General Review of the Current Development of Mechanically Agitated Vessels

Reference 13

Resolution: verified exact; doi, observed 2026-08-06T17:10:55.001148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cb99fd44-2251-485e-b28c-d5e3b4e77816 · outbound

This paper cites NSFnets (Navier-Stokes Flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equa- tions.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks NSFnets (Navier-Stokes Flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equa- tions

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:50.876982Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation adfc7cc2-2a14-4ff3-bb0f-f9d4c16f325b · outbound

This paper cites Joshi, Nandkishor K.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Joshi, Nandkishor K

Reference 15

Resolution: verified exact; doi, observed 2026-08-06T17:10:54.798631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6ae8ceb0-c382-4ef7-8b4e-39e8e359dc69 · outbound

This paper cites Fotiadis.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Fotiadis

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:58.838523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d05b4abc-c242-48b4-af2a-cfb16b3a0399 · outbound

This paper cites Lorenzen, A.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Lorenzen, A

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:51.259504Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a2b7ec2f-7e75-4418-afe5-c06a6841dcfe · outbound

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

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 18

Resolution: malformed identifier; no resolver link, observed 2026-08-06T17:10:51.351981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a680da3-b8b1-4f50-902f-28ea678bcc71 · outbound

This paper cites McClenny and Ulisses M.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks McClenny and Ulisses M

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:51.457983Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9517442a-a0c1-4e56-b235-84d184b4bad6 · outbound

This paper cites Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equa- tions.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equa- tions

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:58.623754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dfa78386-35fc-41b4-8c7d-4b0121e3d5dc · outbound

This paper cites Raissi, P.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Raissi, P

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:51.685738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 77567535-7e56-46e2-8583-2c74a7e2b6e0 · outbound

This paper cites Hidden fluid me- chanics: Learning velocity and pressure fields from flow visualizations.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Hidden fluid me- chanics: Learning velocity and pressure fields from flow visualizations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:51.732891Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38bf7f9b-eb42-44ba-8ab8-240ccd421a3f · outbound

This paper cites CFD simulation of a Rushton turbine stirred-tank using open-source software with critical evaluation of MRF-based rotation modeling.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks CFD simulation of a Rushton turbine stirred-tank using open-source software with critical evaluation of MRF-based rotation modeling

Reference 23

Resolution: verified exact; doi, observed 2026-08-06T17:10:54.568001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 121bfa2a-4826-427a-a932-e9d05201f729 · outbound

This paper cites Rosseburg, J.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Rosseburg, J

Reference 24

Resolution: verified exact; doi, observed 2026-08-06T17:10:54.395840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 03720c36-3c69-400e-8f55-85159531cae4 · outbound

This paper cites PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:51.987513Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a215180-903b-462b-9626-4d58b5f71c7f · outbound

This paper cites Jagtap, and George Em Karniadakis.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Jagtap, and George Em Karniadakis

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:58.402565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b4548577-6230-438f-bda5-80f5553f4c19 · outbound

This paper cites Steinfurth, A.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Steinfurth, A

Reference 27

Resolution: verified exact; doi, observed 2026-08-06T17:10:54.155554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 921c8935-1815-467d-870a-32a32dd273e1 · outbound

This paper cites Shape-optimization of extrusion-dies via parameterized physics-informed neural networks.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Shape-optimization of extrusion-dies via parameterized physics-informed neural networks

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:58.181928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3c4a9307-92db-4371-a435-77397ee17b61 · outbound

This paper cites A model hierarchy for predicting the flow in stirred tanks with physics-informed neu- ral networks.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks A model hierarchy for predicting the flow in stirred tanks with physics-informed neu- ral networks

Reference 29

Resolution: verified exact; doi, observed 2026-08-06T17:10:53.788808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 15f38db0-03ee-4203-8615-acb6e69c7e45 · outbound

This paper cites PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks, November 2024.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks, November 2024

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:57.984593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 38b9e8a1-7ff1-40dd-8515-d5245f8df39f · outbound

This paper cites Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:52.606872Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dde889d2-dc3e-4c76-873e-77458dcda851 · outbound

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

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks An Expert's Guide to Training Physics-informed Neural Networks

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:52.698302Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c83c1fc4-9e8e-488c-ad43-737c0e7f6389 · outbound

This paper cites Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective, February 2025.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective, February 2025

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:57.680190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1dee9bba-f6fa-491e-93d7-4f6fa3cc11b3 · outbound

This paper cites A comprehensive study of non- adaptive and residual-based adaptive sampling for physics-informed neural networks.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks A comprehensive study of non- adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:52.864434Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46553b03-052b-4cca-b30a-7726c767cf48 · outbound

This paper cites Hy- brid Modeling of Fed-Batch Cell Culture Using Physics-Informed Neural Network.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Hy- brid Modeling of Fed-Batch Cell Culture Using Physics-Informed Neural Network

Reference 35

Resolution: verified exact; doi, observed 2026-08-06T17:10:53.586753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6e8a6446-1047-4a2d-83b5-145fc43f4b9d · outbound

This paper cites MultiAdam: Parameter-wise scale-invariant optimizer for multiscale training of physics-informed neural net- works.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks MultiAdam: Parameter-wise scale-invariant optimizer for multiscale training of physics-informed neural net- works

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:57.482878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 861bebf0-b8be-454b-aace-b3748168c73c · outbound

This paper cites Non-intrusive reduced-order modeling for fluid prob- lems: A brief review.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Non-intrusive reduced-order modeling for fluid prob- lems: A brief review

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:53.206207Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6be04700-541b-4489-bc07-9122aa346247 · outbound

This paper cites Gambaruto.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Gambaruto

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:57.190292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7a2e06ae-6815-4381-96c2-8552e0f459f9 · outbound

This paper cites Physics-Informed Neural Networks with Complementary Soft and Hard Constraints for Solving Complex Boundary Navier-Stokes Equations, November 2024.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Physics-Informed Neural Networks with Complementary Soft and Hard Constraints for Solving Complex Boundary Navier-Stokes Equations, November 2024

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:10:56.936815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation daf4f0b2-4d59-43cf-9e87-ea536093d447 · outbound

This paper cites doi: 10.1109/72.712178.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks doi: 10.1109/72.712178

Reference 1998

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:51.184721Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1de786a9-63b7-43f2-9786-0b876ca7c9d0 · outbound

This paper cites doi: 10.1016/j.jcp.2021.110683.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks doi: 10.1016/j.jcp.2021.110683

Reference 2021

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T17:10:56.068682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3a5e7d41-8119-4710-a674-7ad6f3a68471 · outbound

This paper cites doi: 10.1002/pamm.202300203.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks doi: 10.1002/pamm.202300203

Reference 2023

Resolution: verified exact; doi, observed 2026-08-06T17:10:53.996137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b1f5471c-5bbc-4b12-be1e-d9818f537868 · outbound

This paper cites an unresolved cited work.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Unresolved cited work

Reference 7691

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:49.653580Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 461c4219-e765-4565-adbb-d8b3e43b2c2e · outbound

This paper cites an unresolved cited work.

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks Unresolved cited work

Reference 9044

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:51.600965Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Coverage vector

Reference resolution

Outbound references

Pith citing papers