{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T05:26:58Z","timestamp":1769318818127,"version":"3.49.0"},"reference-count":49,"publisher":"ASME International","issue":"7","license":[{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.asme.org\/publications-submissions\/publishing-information\/legal-policies"}],"funder":[{"DOI":"10.13039\/501100005950","name":"Hong Kong University of Science and Technology","doi-asserted-by":"publisher","award":["OKT24EG05"],"award-info":[{"award-number":["OKT24EG05"]}],"id":[{"id":"10.13039\/501100005950","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001839","name":"University Grants Committee","doi-asserted-by":"publisher","award":["RMGS24EG04"],"award-info":[{"award-number":["RMGS24EG04"]}],"id":[{"id":"10.13039\/501100001839","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Fluid dynamics is governed by partial differential equations (PDEs) which are solved numerically. The limitations of traditional methods in data assimilation hinder their effective engagement with experiments. Physics-informed neural network (PINN) has emerged as a hybrid data-physics-driven model for convective problems. However, the approach suffers from low accuracy and poor efficiency due to the way of incorporating PDEs. In this work, a novel convolutional neural network framework integrating the finite volume method (FVM) is developed to address the challenge. The interface variables of the grid are predicted by the neural network for the first time, rather than a complex procedure in FVM. The physical law is then learned by minimizing the residual of the discretized conservative form of PDEs. A comparison between this model and the existing PINN models regarding prediction accuracy demonstrates the superiority of embedding PDEs through FVM. The effects of sampling strategies and quantities are studied. The result confirms the model's capability to utilize sparse measurement data within the computational domain. Furthermore, the model performs well even in scenarios where partial initial and boundary conditions are absent.<\/jats:p>","DOI":"10.1115\/1.4067583","type":"journal-article","created":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T15:41:26Z","timestamp":1736437286000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":5,"title":["Finite-Volume Physics-Informed U-Net for Flow Field Reconstruction With Sparse Data"],"prefix":"10.1115","volume":"25","author":[{"given":"Tong","family":"Zhu","sequence":"first","affiliation":[{"name":"The Hong Kong University of Science and Technology Department of Mechanicaland Aerospace Engineering, , Clear Water Bay, , ,","place":["Hong Kong, SAR, China, 999077"]}]},{"given":"Dehao","family":"Liu","sequence":"additional","affiliation":[{"name":"State University of New York at Binghamton Department of Mechanical Engineering, , , \u00a0","place":["Binghamton, NY, 13902"]}]},{"given":"Yanglong","family":"Lu","sequence":"additional","affiliation":[{"name":"The Hong Kong University of Science and Technology Department of Mechanicaland Aerospace Engineering, , Clear Water Bay, , ,","place":["Hong Kong, SAR, China, 999077"]}]}],"member":"33","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"key":"2025040314093208200_CIT0001","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1155\/2022\/4985193","article-title":"Numerical Simulation of Ground Effect on Circulation Control Airfoil","volume":"2022","author":"Sun","year":"2022","journal-title":"Int. J. Aerosp. Eng."},{"issue":"2","key":"2025040314093208200_CIT0002","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/s10237-022-01556-7","article-title":"Fluid-Structure Interaction Simulation of Tissue Degradation and its Effects on Intra-Aneurysm Hemodynamics","volume":"21","author":"Wang","year":"2022","journal-title":"Biomech. Model. Mechanobiol."},{"key":"2025040314093208200_CIT0003","doi-asserted-by":"publisher","first-page":"117950","DOI":"10.1016\/j.ces.2022.117950","article-title":"Numerical Investigation of Bio-Inspired Mixing Enhancement for Enzymatic Hydrolysis","volume":"260","author":"Zhu","year":"2022","journal-title":"Chem. Eng. Sci."},{"key":"2025040314093208200_CIT0004","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.cpc.2019.06.013","article-title":"A Very-High-Order TENO Scheme for All-Speed Gas Dynamics and Turbulence","volume":"244","author":"Fu","year":"2019","journal-title":"Comput. Phys. Commun."},{"key":"2025040314093208200_CIT0005","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1186\/s13662-018-1876-4","article-title":"Finite Difference Scheme for Simulating a Generalized Two-Dimensional Multi-Term Time Fractional Non-Newtonian Fluid Model","volume":"2018","author":"Liu","year":"2018","journal-title":"Adv. Differ. Eq."},{"key":"2025040314093208200_CIT0006","doi-asserted-by":"publisher","first-page":"104148","DOI":"10.1016\/j.jnnfm.2019.104148","article-title":"An Adaptive Finite Element Method for Elastoviscoplastic Fluid Flows","volume":"271","author":"Chaparian","year":"2019","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"2025040314093208200_CIT0007","doi-asserted-by":"publisher","first-page":"107182","DOI":"10.1016\/j.ijthermalsci.2021.107182","article-title":"Prediction of Heat Transfer Coefficient and Friction Factor of Mini Channel Shell and Tube Heat Exchanger Using Numerical Analysis and Experimental Validation","volume":"171","author":"\u00dcnverdi","year":"2022","journal-title":"Int. J. Therm. Sci."},{"issue":"8","key":"2025040314093208200_CIT0008","doi-asserted-by":"publisher","first-page":"3299","DOI":"10.2514\/1.J058990","article-title":"Physics-Based Compressive Sensing Approach to Monitor Turbulent Flow","volume":"58","author":"Lu","year":"2020","journal-title":"AIAA J."},{"key":"2025040314093208200_CIT0009","doi-asserted-by":"publisher","first-page":"102304","DOI":"10.1016\/j.addma.2021.102304","article-title":"Physics Based Compressive Sensing to Monitor Temperature and Melt Flow in Laser Powder Bed Fusion","volume":"47","author":"Lu","year":"2021","journal-title":"Addit. Manuf."},{"key":"2025040314093208200_CIT0010","doi-asserted-by":"publisher","first-page":"111120","DOI":"10.1016\/j.ymssp.2024.111120","article-title":"A Review on Physics-Informed Data-Driven Remaining Useful Life Prediction: Challenges and Opportunities","volume":"209","author":"Li","year":"2024","journal-title":"Mech. Syst. Signal Process."},{"issue":"4","key":"2025040314093208200_CIT0011","doi-asserted-by":"publisher","first-page":"041012","DOI":"10.1115\/1.4053800","article-title":"Solving Inverse Heat Transfer Problems Without Surrogate Models: A Fast, Data-Sparse, Physics Informed Neural Network Approach","volume":"22","author":"Oommen","year":"2022","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"key":"2025040314093208200_CIT0012","doi-asserted-by":"publisher","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":"2025040314093208200_CIT0013","doi-asserted-by":"publisher","first-page":"114502","DOI":"10.1016\/j.cma.2021.114502","article-title":"Physics-Informed Graph Neural Galerkin Networks: A Unified Framework for Solving PDE-Governed Forward and Inverse Problems","volume":"390","author":"Gao","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2025040314093208200_CIT0014","doi-asserted-by":"publisher","first-page":"113722","DOI":"10.1016\/j.cma.2021.113722","article-title":"DiscretizationNet: A Machine-Learning Based Solver for Navier\u2013Stokes Equations Using Finite Volume Discretization","volume":"378","author":"Ranade","year":"2021","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2025040314093208200_CIT0015","doi-asserted-by":"publisher","first-page":"112702","DOI":"10.1016\/j.jcp.2023.112702","article-title":"Artificial Neural Network-Augmented Stabilized Finite Element Method","volume":"499","author":"Yadav","year":"2024","journal-title":"J. Comput. Phys."},{"key":"2025040314093208200_CIT0016","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.jcp.2019.05.024","article-title":"Physics-Constrained Deep Learning for High-Dimensional Surrogate Modeling and Uncertainty Quantification Without Labeled Data","volume":"394","author":"Zhu","year":"2019","journal-title":"J. Comput. Phys."},{"key":"2025040314093208200_CIT0017","doi-asserted-by":"publisher","first-page":"113284","DOI":"10.1016\/j.jcp.2024.113284","article-title":"f-PICNN: A Physics-Informed Convolutional Neural Network for Partial Differential Equations With Space-Time Domain","volume":"515","author":"Yuan","year":"2024","journal-title":"J. Comput. Phys."},{"issue":"12","key":"2025040314093208200_CIT0018","doi-asserted-by":"publisher","first-page":"033149","DOI":"10.1029\/2022WR033149","article-title":"Learning Groundwater Contaminant Diffusion-Sorption Processes With a Finite Volume Neural Network","volume":"58","author":"Praditia","year":"2022","journal-title":"Water Resour. Res."},{"issue":"3","key":"2025040314093208200_CIT0019","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1007\/s11831-017-9213-8","article-title":"A Higher-Order Chimera Method for Finite Volume Schemes","volume":"25","author":"Ram\u00edrez","year":"2018","journal-title":"Arch. Comput. Methods Eng."},{"key":"2025040314093208200_CIT0020","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/j.jcp.2015.10.014","article-title":"A New Efficient Formulation of the HLLEM Riemann Solver for General Conservative and Non-Conservative Hyperbolic Systems","volume":"304","author":"Dumbser","year":"2016","journal-title":"J. Comput. Phys."},{"key":"2025040314093208200_CIT0021","doi-asserted-by":"publisher","first-page":"105774","DOI":"10.1016\/j.compfluid.2022.105774","article-title":"A Constrained Boundary Gradient Reconstruction Method for Unstructured Finite Volume Discretization of the Euler Equations","volume":"252","author":"Wei","year":"2023","journal-title":"Comput. Fluids"},{"key":"2025040314093208200_CIT0022","doi-asserted-by":"publisher","first-page":"112300","DOI":"10.1016\/j.jcp.2023.112300","article-title":"Three-Dimensional High-Order Finite-Volume Method Based on Compact WENO Reconstruction With Hybrid Unstructured Grids","volume":"490","author":"Zhan","year":"2023","journal-title":"J. Comput. Phys."},{"key":"2025040314093208200_CIT0023","doi-asserted-by":"publisher","first-page":"105899","DOI":"10.1016\/j.compfluid.2023.105899","article-title":"A Unified Consistent Source Term Computational Algorithm for the \u03b3-Based Compressible Multi-Fluid Flow Model","volume":"259","author":"Ge","year":"2023","journal-title":"Comput. Fluids"},{"key":"2025040314093208200_CIT0024","doi-asserted-by":"publisher","first-page":"104591","DOI":"10.1016\/j.compfluid.2020.104591","article-title":"An Improved Roe Solver for High Order Reconstruction Schemes","volume":"207","author":"Musa","year":"2020","journal-title":"Comput. Fluids"},{"key":"2025040314093208200_CIT0025","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.amc.2019.03.001","article-title":"Towards Optimal High-Order Compact Schemes for Simulating Compressible Flows","volume":"355","author":"Zhang","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"2025040314093208200_CIT0026","doi-asserted-by":"publisher","first-page":"110547","DOI":"10.1016\/j.jcp.2021.110547","article-title":"Multidimensional Approximate Riemann Solvers for Hyperbolic Nonconservative Systems. Applications to Shallow Water Systems","volume":"444","author":"Schneider","year":"2021","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2025040314093208200_CIT0027","doi-asserted-by":"publisher","first-page":"027110","DOI":"10.1063\/5.0084547","article-title":"An Efficient Discrete Velocity Method With Inner Iteration for Steady Flows in All Flow Regimes","volume":"34","author":"Yang","year":"2022","journal-title":"Phys. Fluids"},{"key":"2025040314093208200_CIT0028","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.ecoinf.2018.10.002","article-title":"Deep Convolution Neural Network for Image Recognition","volume":"48","author":"Traore","year":"2018","journal-title":"Ecol. Inf."},{"key":"2025040314093208200_CIT0029","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.neucom.2018.03.037","article-title":"Methods and Datasets on Semantic Segmentation: A Review","volume":"304","author":"Yu","year":"2018","journal-title":"Neurocomputing"},{"key":"2025040314093208200_CIT0030","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1613\/jair.4992","article-title":"A Primer on Neural Network Models for Natural Language Processing","volume":"57","author":"Goldberg","year":"2016","journal-title":"J. Artif. Intell. Res."},{"issue":"6","key":"2025040314093208200_CIT0031","doi-asserted-by":"publisher","first-page":"061007","DOI":"10.1115\/1.4047173","article-title":"Physics-Informed Neural Networks for Missing Physics Estimation in Cumulative Damage Models: A Case Study in Corrosion Fatigue","volume":"20","author":"Dourado","year":"2020","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"4","key":"2025040314093208200_CIT0032","doi-asserted-by":"publisher","first-page":"040802","DOI":"10.1115\/1.4064449","article-title":"Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics","volume":"24","author":"Faroughi","year":"2024","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"1","key":"2025040314093208200_CIT0033","doi-asserted-by":"publisher","first-page":"7","DOI":"10.11648\/j.ajnna.20190501.12","article-title":"An Overview of Neural Network","volume":"5","author":"Islam","year":"2019","journal-title":"Am. J. Neural Netw. Appl."},{"issue":"11","key":"2025040314093208200_CIT0034","doi-asserted-by":"publisher","first-page":"111002","DOI":"10.1115\/1.4063863","article-title":"A Physics-Informed General Convolutional Network for the Computational Modeling of Materials With Damage","volume":"24","author":"Janssen","year":"2024","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"4","key":"2025040314093208200_CIT0035","doi-asserted-by":"publisher","first-page":"3439","DOI":"10.1007\/s11071-021-06819-z","article-title":"Solving Huxley Equation Using an Improved PINN Method","volume":"105","author":"Bai","year":"2021","journal-title":"Nonlinear Dyn."},{"issue":"3","key":"2025040314093208200_CIT0036","doi-asserted-by":"publisher","first-page":"031008","DOI":"10.1115\/1.4055316","article-title":"Multifidelity Physics-Constrained Neural Networks With Minimax Architecture","volume":"23","author":"Liu","year":"2023","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"1","key":"2025040314093208200_CIT0037","doi-asserted-by":"publisher","first-page":"011012","DOI":"10.1115\/1.4055924","article-title":"Physics-Constrained Bayesian Neural Network for Bias and Variance Reduction","volume":"23","author":"Malashkhia","year":"2022","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"3","key":"2025040314093208200_CIT0038","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.taml.2020.01.039","article-title":"Physics-Informed Deep Learning for Incompressible Laminar Flows","volume":"10","author":"Rao","year":"2020","journal-title":"Theoret. Appl. Mech. Lett."},{"issue":"7","key":"2025040314093208200_CIT0039","doi-asserted-by":"publisher","first-page":"071905","DOI":"10.1063\/5.0055600","article-title":"Uncovering Near-Wall Blood Flow From Sparse Data With Physics-Informed Neural Networks","volume":"33","author":"Arzani","year":"2021","journal-title":"Phys. Fluids"},{"key":"2025040314093208200_CIT0040","doi-asserted-by":"publisher","first-page":"106164","DOI":"10.1016\/j.compfluid.2023.106164","article-title":"Physics-Informed Neural Networks for Parametric Compressible Euler Equations","volume":"270","author":"Wassing","year":"2024","journal-title":"Comput. Fluids"},{"key":"2025040314093208200_CIT0041","doi-asserted-by":"publisher","first-page":"111402","DOI":"10.1016\/j.jcp.2022.111402","article-title":"Physics-Informed Neural Networks for Inverse Problems in Supersonic Flows","volume":"466","author":"Jagtap","year":"2022","journal-title":"J. Comput. Phys."},{"issue":"6","key":"2025040314093208200_CIT0042","doi-asserted-by":"publisher","DOI":"10.1115\/1.4046892","article-title":"Solution of Biharmonic Equation in Complicated Geometries With Physics Informed Extreme Learning Machine","volume":"20","author":"Dwivedi","year":"2020","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"4","key":"2025040314093208200_CIT0043","doi-asserted-by":"publisher","first-page":"044501","DOI":"10.1115\/1.4053671","article-title":"Using Physics-Informed Generative Adversarial Networks to Perform Super-Resolution for Multiphase Fluid Simulations","volume":"22","author":"Li","year":"2022","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"8","key":"2025040314093208200_CIT0044","doi-asserted-by":"publisher","first-page":"087117","DOI":"10.1063\/5.0161114","article-title":"Physics-Informed Graph Convolutional Neural Network for Modeling Fluid Flow and Heat Convection","volume":"35","author":"Peng","year":"2023","journal-title":"Phys. Fluids"},{"issue":"6","key":"2025040314093208200_CIT0045","doi-asserted-by":"publisher","first-page":"7406","DOI":"10.1002\/nme.7406","article-title":"RoeNet: Predicting Discontinuity of Hyperbolic Systems From Continuous Data","volume":"125","author":"Tong","year":"2024","journal-title":"Int. J. Numer. Methods Eng."},{"key":"2025040314093208200_CIT0046","doi-asserted-by":"publisher","first-page":"114399","DOI":"10.1016\/j.cma.2021.114399","article-title":"PhyCRNet: Physics-Informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs","volume":"389","author":"Ren","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2025040314093208200_CIT0047","doi-asserted-by":"publisher","first-page":"82031","DOI":"10.1109\/ACCESS.2021.3086020","article-title":"U-net and Its Variants for Medical Image Segmentation: A Review of Theory and Applications","volume":"9","author":"Siddique","year":"2021","journal-title":"IEEE Access"},{"issue":"4","key":"2025040314093208200_CIT0048","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1007\/s00530-020-00726-w","article-title":"FU-Net: Fast Biomedical Image Segmentation Model Based on Bottleneck Convolution Layers","volume":"27","author":"Olimov","year":"2021","journal-title":"Multimedia Syst."},{"issue":"11","key":"2025040314093208200_CIT0049","doi-asserted-by":"publisher","first-page":"111004","DOI":"10.1115\/1.4064555","article-title":"Physics-Informed Fully Convolutional Networks for Forward Prediction of Temperature Field and Inverse Estimation of Thermal Diffusivity","volume":"24","author":"Zhu","year":"2024","journal-title":"ASME J. Comput. Inf. Sci. Eng."}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4067583\/7422303\/jcise-24-1431.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4067583\/7422303\/jcise-24-1431.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T18:25:35Z","timestamp":1743704735000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/25\/7\/071004\/1211157\/Finite-Volume-Physics-Informed-U-Net-for-Flow"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,3]]},"references-count":49,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2025,7,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4067583","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,3]]},"article-number":"071004"}}