{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T11:10:29Z","timestamp":1779102629385,"version":"3.51.4"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,4,6]],"date-time":"2023-04-06T00:00:00Z","timestamp":1680739200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,6]],"date-time":"2023-04-06T00:00:00Z","timestamp":1680739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s00366-023-01814-x","type":"journal-article","created":{"date-parts":[[2023,4,6]],"date-time":"2023-04-06T15:17:48Z","timestamp":1680794268000},"page":"3773-3789","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Comparative study of modelling flows in porous media for engineering applications using finite volume and artificial neural network methods"],"prefix":"10.1007","volume":"39","author":[{"given":"Pijus","family":"Makauskas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mayur","family":"Pal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vismay","family":"Kulkarni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abhishek Singh","family":"Kashyap","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Himanshu","family":"Tyagi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,4,6]]},"reference":[{"key":"1814_CR1","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1006\/jcph.1993.1072","volume":"1","author":"LJ Durlofsky","year":"1993","unstructured":"Durlofsky LJ (1993) A triangle based mixed finite element finite volume technique for modeling two phase flow through porous media. J Comput Phys 1:252\u2013266","journal-title":"J Comput Phys"},{"key":"1814_CR2","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1023\/A:1021243231313","volume":"6","author":"MG Edwards","year":"2002","unstructured":"Edwards MG (2002) Unstructured, control-volume distributed, full-tensor finite volume schemes with flow based grids. Comput Geo 6:433\u2013452","journal-title":"Comput Geo"},{"key":"1814_CR3","doi-asserted-by":"crossref","unstructured":"Eigestad GT, Klausen RA (2005) On convergence of multi-point flux approximation o-method; numerical experiment for discontinuous permeability. (2nd\u00a0edn). Submitted to Numer Meth Part Diff Eqs","DOI":"10.1002\/num.20079"},{"key":"1814_CR4","doi-asserted-by":"publisher","unstructured":"Guo X, Li W, Iorio F (2016) Convolutional neural networks for steady flow approximation. https:\/\/doi.org\/10.1145\/2939672.2939738","DOI":"10.1145\/2939672.2939738"},{"key":"1814_CR5","volume-title":"Neural Network Design","author":"MT Hagan","year":"1996","unstructured":"Hagan MT, Demuth HB, Beale MH (1996) Neural Network Design. PWS Publishing, Boston"},{"key":"1814_CR6","doi-asserted-by":"publisher","unstructured":"Li Z, Kovachki N, Azizzadenesheli K, Liu B, Bhattacharya K, Stuart A, Anandkumar A (2021) Fourier neural operator for parametric partial differential equations. https:\/\/doi.org\/10.48550\/arXiv.2010.08895.","DOI":"10.48550\/arXiv.2010.08895."},{"key":"1814_CR7","doi-asserted-by":"publisher","unstructured":"Pal M, Makauskas P, Malik S (2023) Upscaling porous media using neural networks: a deep learning approach to homogenization and averaging. https:\/\/doi.org\/10.3390\/pr11020601","DOI":"10.3390\/pr11020601"},{"key":"1814_CR8","unstructured":"Recktenwald G (2014) The control-volume finite-difference approximation to the diffusion equation"},{"key":"1814_CR9","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1023\/A:1021291114475","volume":"6","author":"I Aavatsmark","year":"2002","unstructured":"Aavatsmark I (2002) Introduction to multipoint flux approximation for quadrilateral grids. Comput Geo No 6:405\u2013432","journal-title":"Comput Geo No"},{"key":"1814_CR10","unstructured":"Kirill Zubov et al. (2021) NeuralPDE: automating physics-informed neural networks (PINNs) with error approximations. http:\/\/arxiv.org\/2107.09443arXiv:https:\/\/arxiv.org\/abs\/2107.09443"},{"key":"1814_CR11","unstructured":"The Julia Programming Language. Version 1.7.3 (2022) Jeff Bezanson, Alan Edelman, Viral B. Shah and Stefan Karpinski, 2009, https:\/\/julialang.org\/"},{"key":"1814_CR12","unstructured":"Pal M, Edwards MG (2006) Effective upscaling using a family of flux-continuous, finite-volume schemes for the pressure equation. In Proceedings, ACME 06 Conference, Queens University Belfast, Northern Ireland-UK, pages 127\u2013130"},{"issue":"9\u201310","key":"1814_CR13","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1002\/fld.1211","volume":"51","author":"M Pal","year":"2006","unstructured":"Pal M, Edwards MG, Lamb AR (2006) Convergence study of a family of flux-continuous, Finite-volume schemes for the general tensor pressure equation. Numer Method Fluids 51(9\u201310):1177\u20131203","journal-title":"Numer Method Fluids"},{"key":"1814_CR14","unstructured":"Pal M (2007) Families of control-volume distributed cvd(mpfa) finite volume schemes for the porous medium pressure equation on structured and unstructured grids. PhD Thesis, University of Wales, Swansea-UK"},{"key":"1814_CR15","doi-asserted-by":"crossref","unstructured":"Pal M, Edwards MG (2008) The competing effects of discretization and upscaling - A study using the q-family of CVD-MPFA. ECMOR 2008 - 11th European Conference on the Mathematics of Oil Recovery","DOI":"10.3997\/2214-4609.20146372"},{"key":"1814_CR16","first-page":"1","volume":"68","author":"M Pal","year":"2010","unstructured":"Pal M (2010) The effects of control-volume distributed multi-point flux approximation (CVD-MPFA) on upscaling-A study using the CVD-MPFA schemes. Int J Numer Methods Fluids 68:1","journal-title":"Int J Numer Methods Fluids"},{"issue":"3","key":"1814_CR17","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1002\/fld.2258","volume":"66","author":"M Pal","year":"2011","unstructured":"Pal M, Edwards MG (2011) Non-linear flux-splitting schemes with imposed discrete maximum principle for elliptic equations with highly anisotropic coefficients. Int J Numer Method Fluids 66(3):299\u2013323","journal-title":"Int J Numer Method Fluids"},{"key":"1814_CR18","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2630","author":"M Pal","year":"2012","unstructured":"Pal M (2012) A unified approach to simulation and upscaling of single-phase flow through vuggy carbonates. Intl J Numer Method Fluids. https:\/\/doi.org\/10.1002\/fld.2630","journal-title":"Intl J Numer Method Fluids"},{"key":"1814_CR19","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2492","author":"M Pal","year":"2012","unstructured":"Pal M, Edwards MG (2012) The effects of control-volume distributed multi-point flux approximation (CVD-MPFA) on upscaling-A study using the CVD-MPFA schemes. Int J Numer Methods Fluids. https:\/\/doi.org\/10.1002\/fld.2492","journal-title":"Int J Numer Methods Fluids"},{"key":"1814_CR20","doi-asserted-by":"crossref","unstructured":"Zhang Wenjuan, Kobaisi Al, Mohammed, (2022) On the monotonicity and positivity of physics-informed neural networks for highly anisotropic diffusion equations. MDPI Energ 15:6823","DOI":"10.3390\/en15186823"},{"key":"1814_CR21","unstructured":"Ahmad S Abushaika (2013) Numerical methods for modelling fluid flow in highly heterogeneous and fractured reservoirs"},{"key":"1814_CR22","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1002\/fld.3978","volume":"77","author":"M Pal","year":"2015","unstructured":"Pal M, Lamine S, Lie K-A, Krogstad S (2015) Validation of multiscale mixed finite-element method. Int J Numer Methods Fluids 77:223","journal-title":"Int J Numer Methods Fluids"},{"key":"1814_CR23","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1080\/10916466.2021.1918712","volume":"39","author":"M Pal","year":"2021","unstructured":"Pal M (2021) On application of machine learning method for history matching and forecasting of times series data from hydrocarbon recovery process using water flooding. Petrol Sci Technol 39:15\u201316","journal-title":"Petrol Sci Technol"},{"key":"1814_CR24","doi-asserted-by":"crossref","unstructured":"Pal M, Makauskas P, Saxena P, Patil P (2022) The neural upscaling method for single-phase flow in porous medium. Paper Presented at EAGE-ECMOR 2022 Conference","DOI":"10.3997\/2214-4609.202244021"},{"key":"1814_CR25","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1145\/325165.32524","volume":"19","author":"Perlin Ken","year":"1985","unstructured":"Ken Perlin (1985) An image synthesizer. SIGGRAPH. Comput Graph 19:287\u2013296. https:\/\/doi.org\/10.1145\/325165.32524","journal-title":"Comput Graph"},{"key":"1814_CR26","unstructured":"Ricky TQ, Chen Yulia Rubanova, Jesse Bettencourt, David Duvenaud (2018) Neural ordinary differential equations. 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), Canada"},{"key":"1814_CR27","unstructured":"Vasilyeva M, Tyrylgin A (2018) Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media. arXiv:https:\/\/arxiv.org\/abs\/1810.01586"},{"key":"1814_CR28","volume":"2","author":"J-L Wu","year":"2018","unstructured":"Wu J-L, XioaH Paterson EG (2018) Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework. Phys Rev Fluids 2:073602","journal-title":"Phys Rev Fluids"},{"key":"1814_CR29","doi-asserted-by":"crossref","unstructured":"Russel TF, Wheeler MF (1983) Finite element and finite difference methods for continuous flows in porous media. Chapter 2, in the Mathematics of Reservoir Simulation, R.E. Ewing ed. Front Appl Math SIAM pp 35\u2013106","DOI":"10.1137\/1.9781611971071.ch2"},{"key":"1814_CR30","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","volume":"378","author":"M Raissi","year":"2019","unstructured":"Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686\u2013707","journal-title":"J Comput Phys"},{"key":"1814_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2021.122396","volume":"185","author":"J Zhao","year":"2022","unstructured":"Zhao J, Zhao W, Ma Z, Yong WA, Dong B (2022) Finding models of heat conduction via machine learning. Int J Heat Mass Transfer 185:122396","journal-title":"Int J Heat Mass Transfer"},{"key":"1814_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2019.118491","volume":"143","author":"S Huang","year":"2019","unstructured":"Huang S, Tao B, Li J, Yin Z (2019) On-line heat flux estimation of a nonlinear heat conduction system with complex geometry using a sequential inverse method and artificial neural network. Int J Heat Mass Transfer 143:118491","journal-title":"Int J Heat Mass Transfer"},{"key":"1814_CR33","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.powtec.2020.06.048","volume":"373","author":"Y Wang","year":"2020","unstructured":"Wang Y, Zhang S, Ma Z, Yang Q (2020) Artificial neural network model development for prediction of nonlinear flow in porous media. Powder Technol 373:274\u2013288","journal-title":"Powder Technol"},{"key":"1814_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.molliq.2020.113492","volume":"313","author":"JMN Abad","year":"2020","unstructured":"Abad JMN, Alizadeh R, Fattahi A, Doranehgard MH, Alhajri E, Karimi N (2020) Analysis of transport processes in a reacting flow of hybrid nanofluid around a bluff-body embedded in porous media using artificial neural network and particle swarm optimization. J Mol Liquids 313:113492","journal-title":"J Mol Liquids"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01814-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01814-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01814-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T03:04:05Z","timestamp":1703041445000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01814-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,6]]},"references-count":34,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["1814"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01814-x","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,6]]},"assertion":[{"value":"21 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}