Deep-learning Assisted Extraction of Fluid Velocity from Scalar Signal Transport in a Shallow Microfluidic Channel Article Swipe
Xiao Zeng
,
Chun‐Dong Xue
,
Kejie Chen
,
Qingyun Jiang
,
Kai‐Rong Qin
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2112.00385
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2112.00385
Precise measurement of flow velocity in microfluidic channels is of importance in microfluidic applications, such as quantitative chemical analysis, sample preparation and drug synthesis. However, simple approaches for quickly and precisely measuring the flow velocity in microchannels are still lacking. Herein, we propose a deep neural networks assisted scalar image velocimetry (DNN-SIV) for quick and precise extraction of fluid velocity in a shallow microfluidic channel with a high aspect ratio, which is a basic geometry for cell culture, from a dye concentration field with spatiotemporal gradients. DNN-SIV is built on physics-informed neural networks and residual neural networks that integrate data of scalar field and physics laws to determine the velocity in the height direction. The underlying enforcing physics laws are derived from the Navier-Stokes equation and the scalar transport equation. Apart from this, dynamic concentration boundary condition is adopted to improve the velocity measurement of laminar flow with small Reynolds Number in microchannels. The proposed DNN-SIV is validated and analyzed by numerical simulations. Compared to integral minimization algorithm used in conventional SIV, DNN-SIV is robust to noise in the measured scalar field and more efficiently allowing real-time flow visualization. Furthermore, the fundamental significance of rational construction of concentration field in microchannels is also underscored. The proposed DNN-SIV in this paper is agnostic to initial and boundary conditions that can be a promising velocity measurement approach for many potential applications in microfluidic chips.
Related Topics
Concepts
Scalar (mathematics)
Microfluidics
Scalar field
Reynolds number
Vector field
Velocimetry
Laminar flow
Flow velocity
Fluid dynamics
Mechanics
Computer science
Artificial intelligence
Physics
Flow (mathematics)
Algorithm
Mathematics
Materials science
Geometry
Classical mechanics
Nanotechnology
Turbulence
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2112.00385
- https://arxiv.org/pdf/2112.00385
- OA Status
- green
- References
- 50
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3214840887
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W3214840887Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2112.00385Digital Object Identifier
- Title
-
Deep-learning Assisted Extraction of Fluid Velocity from Scalar Signal Transport in a Shallow Microfluidic ChannelWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-12-01Full publication date if available
- Authors
-
Xiao Zeng, Chun‐Dong Xue, Kejie Chen, Qingyun Jiang, Kai‐Rong QinList of authors in order
- Landing page
-
https://arxiv.org/abs/2112.00385Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2112.00385Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2112.00385Direct OA link when available
- Concepts
-
Scalar (mathematics), Microfluidics, Scalar field, Reynolds number, Vector field, Velocimetry, Laminar flow, Flow velocity, Fluid dynamics, Mechanics, Computer science, Artificial intelligence, Physics, Flow (mathematics), Algorithm, Mathematics, Materials science, Geometry, Classical mechanics, Nanotechnology, TurbulenceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
50Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W3214840887 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2112.00385 |
| ids.doi | https://doi.org/10.48550/arxiv.2112.00385 |
| ids.mag | 3214840887 |
| ids.openalex | https://openalex.org/W3214840887 |
| fwci | |
| type | preprint |
| title | Deep-learning Assisted Extraction of Fluid Velocity from Scalar Signal Transport in a Shallow Microfluidic Channel |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11255 |
| topics[0].field.id | https://openalex.org/fields/22 |
| topics[0].field.display_name | Engineering |
| topics[0].score | 0.9994000196456909 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2204 |
| topics[0].subfield.display_name | Biomedical Engineering |
| topics[0].display_name | Microfluidic and Bio-sensing Technologies |
| topics[1].id | https://openalex.org/T10412 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9975000023841858 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2204 |
| topics[1].subfield.display_name | Biomedical Engineering |
| topics[1].display_name | Microfluidic and Capillary Electrophoresis Applications |
| topics[2].id | https://openalex.org/T11206 |
| topics[2].field.id | https://openalex.org/fields/31 |
| topics[2].field.display_name | Physics and Astronomy |
| topics[2].score | 0.9940999746322632 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/3109 |
| topics[2].subfield.display_name | Statistical and Nonlinear Physics |
| topics[2].display_name | Model Reduction and Neural Networks |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C57691317 |
| concepts[0].level | 2 |
| concepts[0].score | 0.6598010659217834 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1289248 |
| concepts[0].display_name | Scalar (mathematics) |
| concepts[1].id | https://openalex.org/C8673954 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6377559900283813 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q138845 |
| concepts[1].display_name | Microfluidics |
| concepts[2].id | https://openalex.org/C110521144 |
| concepts[2].level | 2 |
| concepts[2].score | 0.5939446687698364 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q193460 |
| concepts[2].display_name | Scalar field |
| concepts[3].id | https://openalex.org/C182748727 |
| concepts[3].level | 3 |
| concepts[3].score | 0.5815041065216064 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q178932 |
| concepts[3].display_name | Reynolds number |
| concepts[4].id | https://openalex.org/C91188154 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5327154994010925 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q186247 |
| concepts[4].display_name | Vector field |
| concepts[5].id | https://openalex.org/C144836735 |
| concepts[5].level | 2 |
| concepts[5].score | 0.524383008480072 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q7919269 |
| concepts[5].display_name | Velocimetry |
| concepts[6].id | https://openalex.org/C76563973 |
| concepts[6].level | 2 |
| concepts[6].score | 0.4319433569908142 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q189452 |
| concepts[6].display_name | Laminar flow |
| concepts[7].id | https://openalex.org/C166693061 |
| concepts[7].level | 3 |
| concepts[7].score | 0.4281271696090698 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q5462119 |
| concepts[7].display_name | Flow velocity |
| concepts[8].id | https://openalex.org/C90278072 |
| concepts[8].level | 2 |
| concepts[8].score | 0.4198574721813202 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q216320 |
| concepts[8].display_name | Fluid dynamics |
| concepts[9].id | https://openalex.org/C57879066 |
| concepts[9].level | 1 |
| concepts[9].score | 0.39691731333732605 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q41217 |
| concepts[9].display_name | Mechanics |
| concepts[10].id | https://openalex.org/C41008148 |
| concepts[10].level | 0 |
| concepts[10].score | 0.38559719920158386 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[10].display_name | Computer science |
| concepts[11].id | https://openalex.org/C154945302 |
| concepts[11].level | 1 |
| concepts[11].score | 0.35408076643943787 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[11].display_name | Artificial intelligence |
| concepts[12].id | https://openalex.org/C121332964 |
| concepts[12].level | 0 |
| concepts[12].score | 0.34655556082725525 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[12].display_name | Physics |
| concepts[13].id | https://openalex.org/C38349280 |
| concepts[13].level | 2 |
| concepts[13].score | 0.3318970799446106 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q1434290 |
| concepts[13].display_name | Flow (mathematics) |
| concepts[14].id | https://openalex.org/C11413529 |
| concepts[14].level | 1 |
| concepts[14].score | 0.32389509677886963 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[14].display_name | Algorithm |
| concepts[15].id | https://openalex.org/C33923547 |
| concepts[15].level | 0 |
| concepts[15].score | 0.3028034567832947 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[15].display_name | Mathematics |
| concepts[16].id | https://openalex.org/C192562407 |
| concepts[16].level | 0 |
| concepts[16].score | 0.2640748620033264 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[16].display_name | Materials science |
| concepts[17].id | https://openalex.org/C2524010 |
| concepts[17].level | 1 |
| concepts[17].score | 0.24726375937461853 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[17].display_name | Geometry |
| concepts[18].id | https://openalex.org/C74650414 |
| concepts[18].level | 1 |
| concepts[18].score | 0.20587855577468872 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q11397 |
| concepts[18].display_name | Classical mechanics |
| concepts[19].id | https://openalex.org/C171250308 |
| concepts[19].level | 1 |
| concepts[19].score | 0.16521355509757996 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q11468 |
| concepts[19].display_name | Nanotechnology |
| concepts[20].id | https://openalex.org/C196558001 |
| concepts[20].level | 2 |
| concepts[20].score | 0.12022337317466736 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q190132 |
| concepts[20].display_name | Turbulence |
| keywords[0].id | https://openalex.org/keywords/scalar |
| keywords[0].score | 0.6598010659217834 |
| keywords[0].display_name | Scalar (mathematics) |
| keywords[1].id | https://openalex.org/keywords/microfluidics |
| keywords[1].score | 0.6377559900283813 |
| keywords[1].display_name | Microfluidics |
| keywords[2].id | https://openalex.org/keywords/scalar-field |
| keywords[2].score | 0.5939446687698364 |
| keywords[2].display_name | Scalar field |
| keywords[3].id | https://openalex.org/keywords/reynolds-number |
| keywords[3].score | 0.5815041065216064 |
| keywords[3].display_name | Reynolds number |
| keywords[4].id | https://openalex.org/keywords/vector-field |
| keywords[4].score | 0.5327154994010925 |
| keywords[4].display_name | Vector field |
| keywords[5].id | https://openalex.org/keywords/velocimetry |
| keywords[5].score | 0.524383008480072 |
| keywords[5].display_name | Velocimetry |
| keywords[6].id | https://openalex.org/keywords/laminar-flow |
| keywords[6].score | 0.4319433569908142 |
| keywords[6].display_name | Laminar flow |
| keywords[7].id | https://openalex.org/keywords/flow-velocity |
| keywords[7].score | 0.4281271696090698 |
| keywords[7].display_name | Flow velocity |
| keywords[8].id | https://openalex.org/keywords/fluid-dynamics |
| keywords[8].score | 0.4198574721813202 |
| keywords[8].display_name | Fluid dynamics |
| keywords[9].id | https://openalex.org/keywords/mechanics |
| keywords[9].score | 0.39691731333732605 |
| keywords[9].display_name | Mechanics |
| keywords[10].id | https://openalex.org/keywords/computer-science |
| keywords[10].score | 0.38559719920158386 |
| keywords[10].display_name | Computer science |
| keywords[11].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[11].score | 0.35408076643943787 |
| keywords[11].display_name | Artificial intelligence |
| keywords[12].id | https://openalex.org/keywords/physics |
| keywords[12].score | 0.34655556082725525 |
| keywords[12].display_name | Physics |
| keywords[13].id | https://openalex.org/keywords/flow |
| keywords[13].score | 0.3318970799446106 |
| keywords[13].display_name | Flow (mathematics) |
| keywords[14].id | https://openalex.org/keywords/algorithm |
| keywords[14].score | 0.32389509677886963 |
| keywords[14].display_name | Algorithm |
| keywords[15].id | https://openalex.org/keywords/mathematics |
| keywords[15].score | 0.3028034567832947 |
| keywords[15].display_name | Mathematics |
| keywords[16].id | https://openalex.org/keywords/materials-science |
| keywords[16].score | 0.2640748620033264 |
| keywords[16].display_name | Materials science |
| keywords[17].id | https://openalex.org/keywords/geometry |
| keywords[17].score | 0.24726375937461853 |
| keywords[17].display_name | Geometry |
| keywords[18].id | https://openalex.org/keywords/classical-mechanics |
| keywords[18].score | 0.20587855577468872 |
| keywords[18].display_name | Classical mechanics |
| keywords[19].id | https://openalex.org/keywords/nanotechnology |
| keywords[19].score | 0.16521355509757996 |
| keywords[19].display_name | Nanotechnology |
| keywords[20].id | https://openalex.org/keywords/turbulence |
| keywords[20].score | 0.12022337317466736 |
| keywords[20].display_name | Turbulence |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2112.00385 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2112.00385 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2112.00385 |
| locations[1].id | doi:10.48550/arxiv.2112.00385 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | cc-by |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | https://openalex.org/licenses/cc-by |
| locations[1].is_accepted | False |
| locations[1].is_published | |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://doi.org/10.48550/arxiv.2112.00385 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5039845750 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-5638-6545 |
| authorships[0].author.display_name | Xiao Zeng |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Xiao Zeng |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5074825899 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-5259-4491 |
| authorships[1].author.display_name | Chun‐Dong Xue |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Chundong Xue |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5065689413 |
| authorships[2].author.orcid | |
| authorships[2].author.display_name | Kejie Chen |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Kejie Chen |
| authorships[2].is_corresponding | False |
| authorships[3].author.id | https://openalex.org/A5029779278 |
| authorships[3].author.orcid | https://orcid.org/0000-0003-2401-4880 |
| authorships[3].author.display_name | Qingyun Jiang |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Yongjiang Li |
| authorships[3].is_corresponding | False |
| authorships[4].author.id | https://openalex.org/A5090581970 |
| authorships[4].author.orcid | https://orcid.org/0000-0001-6781-2941 |
| authorships[4].author.display_name | Kai‐Rong Qin |
| authorships[4].author_position | last |
| authorships[4].raw_author_name | Kai-Rong Qin |
| authorships[4].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2112.00385 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2021-12-06T00:00:00 |
| display_name | Deep-learning Assisted Extraction of Fluid Velocity from Scalar Signal Transport in a Shallow Microfluidic Channel |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T11255 |
| primary_topic.field.id | https://openalex.org/fields/22 |
| primary_topic.field.display_name | Engineering |
| primary_topic.score | 0.9994000196456909 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2204 |
| primary_topic.subfield.display_name | Biomedical Engineering |
| primary_topic.display_name | Microfluidic and Bio-sensing Technologies |
| related_works | https://openalex.org/W1995680857, https://openalex.org/W2049177871, https://openalex.org/W2070000693, https://openalex.org/W2584042602, https://openalex.org/W2089345006, https://openalex.org/W3046068517, https://openalex.org/W3113444289, https://openalex.org/W2088993275, https://openalex.org/W2888213901, https://openalex.org/W2059317844 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2112.00385 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2112.00385 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2112.00385 |
| primary_location.id | pmh:oai:arXiv.org:2112.00385 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2112.00385 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2112.00385 |
| publication_date | 2021-12-01 |
| publication_year | 2021 |
| referenced_works | https://openalex.org/W2884250335, https://openalex.org/W2106295346, https://openalex.org/W2296761980, https://openalex.org/W2057405362, https://openalex.org/W2058757659, https://openalex.org/W1977941731, https://openalex.org/W2018050443, https://openalex.org/W2161284391, https://openalex.org/W3139279894, https://openalex.org/W1985706996, https://openalex.org/W2161041066, https://openalex.org/W2617378503, https://openalex.org/W2049117454, https://openalex.org/W2551904744, https://openalex.org/W2001607419, https://openalex.org/W1596195796, https://openalex.org/W2194775991, https://openalex.org/W2038943832, https://openalex.org/W2026194129, https://openalex.org/W2001404889, https://openalex.org/W3183360516, https://openalex.org/W2076613928, https://openalex.org/W2047970720, https://openalex.org/W2971115358, https://openalex.org/W1987974907, https://openalex.org/W3137733478, https://openalex.org/W2036827229, https://openalex.org/W2088475009, https://openalex.org/W2095217690, https://openalex.org/W2010546163, https://openalex.org/W3173358212, https://openalex.org/W2070160283, https://openalex.org/W3144086130, https://openalex.org/W2899283552, https://openalex.org/W1533861849, https://openalex.org/W2891481775, https://openalex.org/W3007262342, https://openalex.org/W2980547109, https://openalex.org/W2128380567, https://openalex.org/W1993489284, https://openalex.org/W2086487380, https://openalex.org/W2118449007, https://openalex.org/W1964410631, https://openalex.org/W2086187432, https://openalex.org/W2035159723, https://openalex.org/W2159934755, https://openalex.org/W3080710587, https://openalex.org/W1997088089, https://openalex.org/W2118877935, https://openalex.org/W2964121744 |
| referenced_works_count | 50 |
| abstract_inverted_index.a | 43, 61, 66, 72, 79, 220 |
| abstract_inverted_index.as | 15 |
| abstract_inverted_index.be | 219 |
| abstract_inverted_index.by | 160 |
| abstract_inverted_index.in | 5, 11, 35, 60, 110, 151, 169, 177, 199, 207, 229 |
| abstract_inverted_index.is | 8, 71, 87, 137, 156, 173, 201, 210 |
| abstract_inverted_index.of | 2, 9, 57, 100, 144, 193, 196 |
| abstract_inverted_index.on | 89 |
| abstract_inverted_index.to | 106, 139, 164, 175, 212 |
| abstract_inverted_index.we | 41 |
| abstract_inverted_index.The | 114, 153, 204 |
| abstract_inverted_index.and | 21, 29, 54, 93, 103, 125, 158, 182, 214 |
| abstract_inverted_index.are | 37, 119 |
| abstract_inverted_index.can | 218 |
| abstract_inverted_index.dye | 80 |
| abstract_inverted_index.for | 27, 52, 75, 225 |
| abstract_inverted_index.the | 32, 108, 111, 122, 126, 141, 178, 190 |
| abstract_inverted_index.SIV, | 171 |
| abstract_inverted_index.also | 202 |
| abstract_inverted_index.cell | 76 |
| abstract_inverted_index.data | 99 |
| abstract_inverted_index.deep | 44 |
| abstract_inverted_index.drug | 22 |
| abstract_inverted_index.flow | 3, 33, 146, 187 |
| abstract_inverted_index.from | 78, 121, 131 |
| abstract_inverted_index.high | 67 |
| abstract_inverted_index.laws | 105, 118 |
| abstract_inverted_index.many | 226 |
| abstract_inverted_index.more | 183 |
| abstract_inverted_index.such | 14 |
| abstract_inverted_index.that | 97, 217 |
| abstract_inverted_index.this | 208 |
| abstract_inverted_index.used | 168 |
| abstract_inverted_index.with | 65, 83, 147 |
| abstract_inverted_index.Apart | 130 |
| abstract_inverted_index.basic | 73 |
| abstract_inverted_index.built | 88 |
| abstract_inverted_index.field | 82, 102, 181, 198 |
| abstract_inverted_index.fluid | 58 |
| abstract_inverted_index.image | 49 |
| abstract_inverted_index.noise | 176 |
| abstract_inverted_index.paper | 209 |
| abstract_inverted_index.quick | 53 |
| abstract_inverted_index.small | 148 |
| abstract_inverted_index.still | 38 |
| abstract_inverted_index.this, | 132 |
| abstract_inverted_index.which | 70 |
| abstract_inverted_index.Number | 150 |
| abstract_inverted_index.aspect | 68 |
| abstract_inverted_index.chips. | 231 |
| abstract_inverted_index.height | 112 |
| abstract_inverted_index.neural | 45, 91, 95 |
| abstract_inverted_index.ratio, | 69 |
| abstract_inverted_index.robust | 174 |
| abstract_inverted_index.sample | 19 |
| abstract_inverted_index.scalar | 48, 101, 127, 180 |
| abstract_inverted_index.simple | 25 |
| abstract_inverted_index.DNN-SIV | 86, 155, 172, 206 |
| abstract_inverted_index.Herein, | 40 |
| abstract_inverted_index.Precise | 0 |
| abstract_inverted_index.adopted | 138 |
| abstract_inverted_index.channel | 64 |
| abstract_inverted_index.derived | 120 |
| abstract_inverted_index.dynamic | 133 |
| abstract_inverted_index.improve | 140 |
| abstract_inverted_index.initial | 213 |
| abstract_inverted_index.laminar | 145 |
| abstract_inverted_index.physics | 104, 117 |
| abstract_inverted_index.precise | 55 |
| abstract_inverted_index.propose | 42 |
| abstract_inverted_index.quickly | 28 |
| abstract_inverted_index.shallow | 62 |
| abstract_inverted_index.Compared | 163 |
| abstract_inverted_index.However, | 24 |
| abstract_inverted_index.Reynolds | 149 |
| abstract_inverted_index.agnostic | 211 |
| abstract_inverted_index.allowing | 185 |
| abstract_inverted_index.analyzed | 159 |
| abstract_inverted_index.approach | 224 |
| abstract_inverted_index.assisted | 47 |
| abstract_inverted_index.boundary | 135, 215 |
| abstract_inverted_index.channels | 7 |
| abstract_inverted_index.chemical | 17 |
| abstract_inverted_index.culture, | 77 |
| abstract_inverted_index.equation | 124 |
| abstract_inverted_index.geometry | 74 |
| abstract_inverted_index.integral | 165 |
| abstract_inverted_index.lacking. | 39 |
| abstract_inverted_index.measured | 179 |
| abstract_inverted_index.networks | 46, 92, 96 |
| abstract_inverted_index.proposed | 154, 205 |
| abstract_inverted_index.rational | 194 |
| abstract_inverted_index.residual | 94 |
| abstract_inverted_index.velocity | 4, 34, 59, 109, 142, 222 |
| abstract_inverted_index.(DNN-SIV) | 51 |
| abstract_inverted_index.algorithm | 167 |
| abstract_inverted_index.analysis, | 18 |
| abstract_inverted_index.condition | 136 |
| abstract_inverted_index.determine | 107 |
| abstract_inverted_index.enforcing | 116 |
| abstract_inverted_index.equation. | 129 |
| abstract_inverted_index.integrate | 98 |
| abstract_inverted_index.measuring | 31 |
| abstract_inverted_index.numerical | 161 |
| abstract_inverted_index.potential | 227 |
| abstract_inverted_index.precisely | 30 |
| abstract_inverted_index.promising | 221 |
| abstract_inverted_index.real-time | 186 |
| abstract_inverted_index.transport | 128 |
| abstract_inverted_index.validated | 157 |
| abstract_inverted_index.approaches | 26 |
| abstract_inverted_index.conditions | 216 |
| abstract_inverted_index.direction. | 113 |
| abstract_inverted_index.extraction | 56 |
| abstract_inverted_index.gradients. | 85 |
| abstract_inverted_index.importance | 10 |
| abstract_inverted_index.synthesis. | 23 |
| abstract_inverted_index.underlying | 115 |
| abstract_inverted_index.efficiently | 184 |
| abstract_inverted_index.fundamental | 191 |
| abstract_inverted_index.measurement | 1, 143, 223 |
| abstract_inverted_index.preparation | 20 |
| abstract_inverted_index.velocimetry | 50 |
| abstract_inverted_index.Furthermore, | 189 |
| abstract_inverted_index.applications | 228 |
| abstract_inverted_index.construction | 195 |
| abstract_inverted_index.conventional | 170 |
| abstract_inverted_index.microfluidic | 6, 12, 63, 230 |
| abstract_inverted_index.minimization | 166 |
| abstract_inverted_index.quantitative | 16 |
| abstract_inverted_index.significance | 192 |
| abstract_inverted_index.simulations. | 162 |
| abstract_inverted_index.underscored. | 203 |
| abstract_inverted_index.Navier-Stokes | 123 |
| abstract_inverted_index.applications, | 13 |
| abstract_inverted_index.concentration | 81, 134, 197 |
| abstract_inverted_index.microchannels | 36, 200 |
| abstract_inverted_index.microchannels. | 152 |
| abstract_inverted_index.spatiotemporal | 84 |
| abstract_inverted_index.visualization. | 188 |
| abstract_inverted_index.physics-informed | 90 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |