{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:09:53Z","timestamp":1754154593562,"version":"3.41.2"},"posted":{"date-parts":[[2025]]},"group-title":"SSRN","reference-count":41,"publisher":"Elsevier BV","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.2139\/ssrn.5364744","type":"posted-content","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T12:42:24Z","timestamp":1753360944000},"source":"Crossref","is-referenced-by-count":0,"title":["Surrogate-Based Pressure\u2013Velocity Coupling: Accelerating Incompressible Cfd Flow Solvers with Machine Learning"],"prefix":"10.2139","author":[{"given":"Paulo  Ara\u00fajo da Cunha","family":"Sousa","sequence":"first","affiliation":[]},{"given":"Alexandre  M.","family":"Afonso","sequence":"additional","affiliation":[]},{"given":"Carlos","family":"Veiga Rodrigues","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"ref1","first-page":"73","author":"Cfd","year":"2016","journal-title":"Essentials of Numerical-Methods for"},{"key":"ref2","first-page":"1","article-title":"On the solution of poisson's equation using deep learning","author":"R Aggarwal","year":"2019","journal-title":"13th International Conference on Software, Knowledge, Information Management and Applications (SKIMA)"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1146\/annurev-fluid-010719-060214","article-title":"Machine learning for fluid mechanics","volume":"52","author":"S L Brunton","year":"2020","journal-title":"Annual Review of Fluid Mechanics"},{"key":"ref4","article-title":"Machine learning to speed up computational fluid dynamics engineering simulations for built environments: A review","volume":"267","author":"C Caron","year":"2024","journal-title":"Building and Environment"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.taml.2017.01.005","article-title":"Effect of fluid elasticity on the numerical stability of high-resolution schemes for high shearing contraction flows using openfoam","volume":"7","author":"T Chourushi","year":"2017","journal-title":"Theoretical and Applied Mechanics Letters"},{"journal-title":"Scientific machine learning through physics-informed neural networks: Where we are and what's next","year":"2022","author":"S Cuomo","key":"ref6"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/B978-0-12-220851-5.00007-1","author":"P M Doran","year":"2013","journal-title":"Bioprocess Engineering Principles"},{"volume":"7","year":"2000","author":"R Eymard","key":"ref8"},{"journal-title":"Machine-learning methods for computational science and engineering. Computation","year":"2020","author":"M Frank","key":"ref9"},{"author":"Url","key":"ref10"},{"key":"ref11","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2024.113003","article-title":"Energyconserving neural network for turbulence closure modeling","volume":"508","author":"T Van Gastelen","year":"2024","journal-title":"Journal of Computational Physics"},{"journal-title":"Rans-pinn based simulation surrogates for predicting turbulent flows","year":"2023","author":"S Ghosh","key":"ref12"},{"journal-title":"Indicative results and progress on the development of the unified single solution method for fluid-structure interaction problems","year":"2007","author":"C Giannopapa","key":"ref13"},{"key":"ref14","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/ad6689","article-title":"Turbulence closure modeling with machine learning: a foundational physics perspective","volume":"26","author":"S S Girimaji","year":"2024","journal-title":"New Journal of Physics"},{"key":"ref15","first-page":"481","article-title":"Convolutional neural networks for steady flow approximation","author":"X Guo","year":"2016","journal-title":"Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining"},{"key":"ref16","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijheatfluidflow.2023.109232","article-title":"Studying turbulent flows with physics-informed neural networks and sparse data","volume":"104","author":"S Hanrahan","year":"2023","journal-title":"International Journal of Heat and Fluid Flow"},{"journal-title":"Performance and accuracy assessments of an incompressible fluid solver coupled with a deep convolutional neural network","year":"2021","author":"E A Illarramendi","key":"ref17"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"90099","DOI":"10.1016\/0021-9991(86)90099-9","article-title":"Solution of the implicitly discretised fluid flow equations by operator-splitting","volume":"62","author":"R Issa","year":"1986","journal-title":"Journal of Computational Physics"},{"key":"ref19","first-page":"1","article-title":"Finite element method: an overview","volume":"10","author":"V Jagota","year":"2013","journal-title":"Walailak Journal of Science and Technology"},{"journal-title":"Error analysis and estimation for the finite volume method with applications to fluid flows","year":"1996","author":"H Jasak","key":"ref20"},{"journal-title":"Pythonfoam: In-situ data analyses with openfoam and python","year":"2021","author":"R Maulik","key":"ref21"},{"journal-title":"An implicit gnn solver for poisson-like problems","year":"2023","author":"M Nastorg","key":"ref22"},{"key":"ref23","doi-asserted-by":"crossref","DOI":"10.1145\/3392717.3392772","article-title":"Cfdnet: A deep learning-based accelerator for fluid simulations","author":"O Obiols-Sales","year":"2020","journal-title":"Proceedings of the 34th ACM International Conference on Supercomputing"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"21677","DOI":"10.1007\/s00521-022-07838-6","article-title":"Machine learning-based cfd simulations: a review, models, open threats, and future tactics","volume":"34","author":"D Panchigar","year":"2022","journal-title":"Neural Computing and Applications"},{"key":"ref25","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevFluids.9.034605","article-title":"Turbulence model augmented physics-informed neural networks for mean-flow reconstruction","volume":"9","author":"Y Patel","year":"2024","journal-title":"Phys. Rev. Fluids"},{"key":"ref26","article-title":"Machine learning-based statistical closure models for turbulent dynamical systems","volume":"380","author":"D Qi","year":"2022","journal-title":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physicsinformed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"M Raissi","year":"2019","journal-title":"Journal of Computational Physics"},{"year":"2017","author":"H Schlichting","key":"ref28"},{"journal-title":"Study on a poisson's equation solver based on deep learning technique","year":"2017","author":"T Shan","key":"ref29"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"6725","DOI":"10.1109\/TAP.2020.2985172","article-title":"Study on a fast solver for poisson's equation based on deep learning technique","volume":"68","author":"T Shan","year":"2020","journal-title":"IEEE Transactions on Antennas and Propagation"},{"year":"2023","author":"P Sousa","key":"ref31"},{"key":"ref32","first-page":"1","article-title":"2024a. Application of machine learning to model the pressure poisson equation for fluid flow on generic geometries","volume":"36","author":"P Sousa","journal-title":"Neural Computing and Applications"},{"key":"ref33","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.117133","article-title":"Enhancing cfd solver with machine learning techniques","volume":"429","author":"P Sousa","year":"2024","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"ref34","article-title":"Data-driven, physics-based feature extraction from fluid flow fields using convolutional neural networks","author":"C A M Strofer","year":"2018","journal-title":"Communications in Computational Physics"},{"key":"ref35","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/abadb3","article-title":"Turbulence closure modeling with data-driven techniques: physical compatibility and consistency considerations","volume":"22","author":"S Taghizadeh","year":"2020","journal-title":"New Journal of Physics"},{"journal-title":"An Introduction to Computational Fluid Dynamics: The Finite Volume Method","year":"2007","author":"H Versteeg","key":"ref36"},{"journal-title":"Recent advances on machine learning for computational fluid dynamics: A survey","year":"2024","author":"H Wang","key":"ref37"},{"key":"ref38","article-title":"Data-driven multi-grid solver for accelerated pressure projection","author":"G D Weymouth","year":"2022","journal-title":"Computers &amp Fluids 246, 105620"},{"journal-title":"Solving poisson's equation using deep learning in particle simulation of pn junction","year":"2018","author":"Z Zhang","key":"ref39"},{"key":"ref40","first-page":"63","author":"P B Zhou","year":"1993","journal-title":"Finite Difference Method"},{"journal-title":"Poisson CNN: Convolutional neural networks for the solution","year":"2021","author":"A G \ufffdzbay","key":"ref41"}],"container-title":[],"original-title":[],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T12:53:50Z","timestamp":1753361630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=5364744"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":41,"URL":"https:\/\/doi.org\/10.2139\/ssrn.5364744","relation":{},"subject":[],"published":{"date-parts":[[2025]]},"subtype":"preprint"}}