{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T18:34:01Z","timestamp":1772044441529,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T00:00:00Z","timestamp":1737158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Buildings"],"abstract":"<jats:p>In this work, we propose a Navier\u2013Stokes-Informed Neural Network (NSINN) as a surrogate approach to predict the localized flow behavior of cementitious materials for advancing 3D additive construction technology to gain fundamental insights into multiscale mechanisms of cement paste rheology. NS equations are embedded into the NSINN to interpret the flow pattern in the 3D printing barrel. The results show that the presented NSINN has a higher accuracy compared to a traditional artificial neural network (ANN) as the Mean Square Errors (MSEs) of the u, v, and p predicted by NSINN are 1.25\u00d710\u22124, 1.85\u00d710\u22125, and 3.91\u00d710\u22123, respectively. Compared to the ANN, the MSE of the predictions are 5.88\u00d710\u22122, 4.17\u00d710\u22123, and 1.72\u00d710\u22122, respectively. Moreover, the mean prediction time used in the NSINN, the ANN, and Computational Fluid Dynamics (CFD) are 0.039 s, 0.014 s, and 3.37 s, respectively. That means the method is more computationally efficient at performing simulations compared to CFD which is mesh-based. The NSINN is also utilized in studying the relationship between geometry and extrudability. The ratio (R = 0.25, 0.5, and 0.75) between the diameter of the outlet and that of the domain is studied. It shows that a larger ratio (R = 0.75) can lead to better extrudability of the 3D concrete printing (3DCP).<\/jats:p>","DOI":"10.3390\/buildings15020275","type":"journal-article","created":{"date-parts":[[2025,1,20]],"date-time":"2025-01-20T07:47:37Z","timestamp":1737359257000},"page":"275","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Navier\u2013Stokes-Informed Neural Network for Simulating the Flow Behavior of Flowable Cement Paste in 3D Concrete Printing"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6697-0777","authenticated-orcid":false,"given":"Tianjie","family":"Zhang","sequence":"first","affiliation":[{"name":"Computing PhD Program, Boise State University, Boise, ID 83725, USA"}]},{"given":"Donglei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Boise State University, Boise, ID 83725, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2330-4237","authenticated-orcid":false,"given":"Yang","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Boise State University, Boise, ID 83725, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"118054","DOI":"10.1016\/j.jclepro.2019.118054","article-title":"Rheology and buildability of sustainable cement-based composites containing micro-crystalline cellulose for 3D-printing","volume":"239","author":"Long","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102992","DOI":"10.1016\/j.autcon.2019.102992","article-title":"Mesh reinforcing method for 3D Concrete Printing","volume":"109","author":"Marchment","year":"2020","journal-title":"Autom. Constr."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rehman, A.U., and Kim, J.-H. (2021). 3D concrete printing: A systematic review of rheology, mix designs, mechanical, microstructural, and durability characteristics. Materials, 14.","DOI":"10.3390\/ma14143800"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"104156","DOI":"10.1016\/j.cemconcomp.2021.104156","article-title":"Sustainable materials for 3D concrete printing","volume":"122","author":"Bhattacherjee","year":"2021","journal-title":"Cem. Concr. Compos."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"104060","DOI":"10.1016\/j.cemconcomp.2021.104060","article-title":"Ambient temperature cured \u2018just-add-water\u2019geopolymer for 3D concrete printing applications","volume":"121","author":"Bong","year":"2021","journal-title":"Cem. Concr. Compos."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/j.conbuildmat.2015.05.132","article-title":"Mechanical properties of structures 3D printed with cementitious powders","volume":"93","author":"Feng","year":"2015","journal-title":"Constr. Build. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1016\/j.conbuildmat.2019.07.161","article-title":"Correlation between pore characteristics and tensile bond strength of additive manufactured mortar using X-ray computed tomography","volume":"226","author":"Lee","year":"2019","journal-title":"Constr. Build. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1088\/0965-0393\/11\/4\/307","article-title":"Shear-induced particle migration modelling in a concentrated suspension flow","volume":"11","author":"Chen","year":"2003","journal-title":"Model. Simul. Mater. Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104854","DOI":"10.1016\/j.cemconcomp.2022.104854","article-title":"Rheological characterization of ultra-high performance concrete for 3D printing","volume":"136","author":"Arunothayan","year":"2023","journal-title":"Cem. Concr. Compos."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.conbuildmat.2019.06.224","article-title":"How much is bulk concrete sheared during pumping?","volume":"223","author":"Feys","year":"2019","journal-title":"Constr. Build. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103952","DOI":"10.1016\/j.cemconcomp.2021.103952","article-title":"Effect of flow behavior and process-induced variations on shape stability of 3D printed elements\u2013A review","volume":"118","author":"Vallurupalli","year":"2021","journal-title":"Cem. Concr. Compos."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.cemconres.2012.11.001","article-title":"Lubrication layer properties during concrete pumping","volume":"45","author":"Choi","year":"2013","journal-title":"Cem. Concr. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.cemconres.2011.12.003","article-title":"Hardened properties of high-performance printing concrete","volume":"42","author":"Le","year":"2012","journal-title":"Cem. Concr. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.conbuildmat.2018.04.115","article-title":"Fresh properties of a novel 3D printing concrete ink","volume":"174","author":"Zhang","year":"2018","journal-title":"Constr. Build. Mater."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1126\/science.aaw4741","article-title":"Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations","volume":"367","author":"Raissi","year":"2020","journal-title":"Science"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1090\/S0025-5718-1968-0242392-2","article-title":"Numerical solution of the Navier-Stokes equations","volume":"22","author":"Chorin","year":"1968","journal-title":"Math. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s00466-023-02367-y","article-title":"Numerical simulation of the extrusion and layer deposition processes in 3D concrete printing with the Particle Finite Element Method","volume":"73","author":"Rizzieri","year":"2023","journal-title":"Comput. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"104173","DOI":"10.1016\/j.autcon.2022.104173","article-title":"Extrusion process simulation and layer shape prediction during 3D-concrete-printing using the Particle Finite Element Method","volume":"136","author":"Reinold","year":"2022","journal-title":"Autom. Constr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104075","DOI":"10.1016\/j.cemconcomp.2021.104075","article-title":"Extrusion rheometer for 3D concrete printing","volume":"121","author":"Jayathilakage","year":"2021","journal-title":"Cem. Concr. Compos."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106256","DOI":"10.1016\/j.cemconres.2020.106256","article-title":"Modelling of 3D concrete printing based on computational fluid dynamics","volume":"138","author":"Comminal","year":"2020","journal-title":"Cem. Concr. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107263","DOI":"10.1016\/j.cemconres.2023.107263","article-title":"Computational fluid dynamics modelling and experimental analysis of reinforcement bar integration in 3D concrete printing","volume":"173","author":"Mollah","year":"2023","journal-title":"Cem. Concr. Res."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Amalinadhi, C., Palar, P.S., Stevenson, R., and Zuhal, L. (2022, January 3\u20137). On Physics-Informed Deep Learning for Solving Navier-Stokes Equations. Proceedings of the AIAA SCITECH 2022 Forum, San Diego, CA, USA.","DOI":"10.2514\/6.2022-1436"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"15105","DOI":"10.1109\/TITS.2023.3300312","article-title":"ECSNet: An Accelerated Real-Time Image Segmentation CNN Architecture for Pavement Crack Detection","volume":"24","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4474","DOI":"10.1109\/TITS.2023.3236247","article-title":"Integrated APC-GAN and AttuNet Framework for Automated Pavement Crack Pixel-Level Segmentation: A New Solution to Small Training Datasets","volume":"24","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"105334","DOI":"10.1016\/j.autcon.2024.105334","article-title":"A data-centric strategy to improve performance of automatic pavement defects detection","volume":"160","author":"Zhang","year":"2024","journal-title":"Autom. Constr."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, T., Wang, D., and Lu, Y. (2023). Machine learning-enabled regional multi-hazards risk assessment considering social vulnerability. Sci. Rep., 13.","DOI":"10.1038\/s41598-023-40159-9"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhang, T., Smith, A., Zhai, H., and Lu, Y. (2025). LSTM+ MA: A Time-Series Model for Predicting Pavement IRI. Infrastructures, 10.","DOI":"10.3390\/infrastructures10010010"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1007\/s12205-024-1066-8","article-title":"Benchmark Study on a Novel Online Dataset for Standard Evaluation of Deep Learning-based Pavement Cracks Classification Models","volume":"28","author":"Zhang","year":"2024","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"13665","DOI":"10.1007\/s00521-024-09791-y","article-title":"PINN-CHK: Physics-informed neural network for high-fidelity prediction of early-age cement hydration kinetics","volume":"36","author":"Rahman","year":"2024","journal-title":"Neural Comput. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1038\/s42254-021-00314-5","article-title":"Physics-informed machine learning","volume":"3","author":"Karniadakis","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1137\/19M1274067","article-title":"DeepXDE: A deep learning library for solving differential equations","volume":"63","author":"Lu","year":"2021","journal-title":"SIAM Rev."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Cheng, C., and Zhang, G.-T. (2021). Deep learning method based on physics informed neural network with resnet block for solving fluid flow problems. Water, 13.","DOI":"10.3390\/w13040423"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"060801","DOI":"10.1115\/1.4050542","article-title":"Physics-informed neural networks for heat transfer problems","volume":"143","author":"Cai","year":"2021","journal-title":"J. Heat Transf."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"105266","DOI":"10.1016\/j.compfluid.2021.105266","article-title":"Machine learning for vortex induced vibration in turbulent flow","volume":"235","author":"Bai","year":"2022","journal-title":"Comput. Fluids"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"114909","DOI":"10.1016\/j.cma.2022.114909","article-title":"CAN-PINN: A fast physics-informed neural network based on coupled-automatic\u2013numerical differentiation method","volume":"395","author":"Chiu","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"107157","DOI":"10.1016\/j.cemconres.2023.107157","article-title":"RheologyNet: A physics-informed neural network solution to evaluate the thixotropic properties of cementitious materials","volume":"168","author":"Zhang","year":"2023","journal-title":"Cem. Concr. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1090\/S0025-5718-1980-0572855-7","article-title":"Updating quasi-Newton matrices with limited storage","volume":"35","author":"Nocedal","year":"1980","journal-title":"Math. Comput."}],"container-title":["Buildings"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-5309\/15\/2\/275\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:31:20Z","timestamp":1759919480000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-5309\/15\/2\/275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,18]]},"references-count":37,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["buildings15020275"],"URL":"https:\/\/doi.org\/10.3390\/buildings15020275","relation":{},"ISSN":["2075-5309"],"issn-type":[{"value":"2075-5309","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,18]]}}}