Physics-informed neural networks (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Physics-informed neural networks" in English language version.

Last modified: 01:07:58, 16 August 2026 (UTC)

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4034doi.org

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3725arxiv.org

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2118adsabs.harvard.edu

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43sciencedirect.com

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32osti.gov

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22openreview.net

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11projecteuclid.org

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11swan.ac.uk

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11creativecommons.org

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adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ui.adsabs.harvard.edu

Arzani, Amirhossein; Wang, Jian-Xun; D'Souza, Roshan M. (2021-06-07). "Uncovering near-wall blood flow from sparse data with physics-informed neural networks". Physics of Fluids. 33 (7): 071905. arXiv:2104.08249. Bibcode:2021PhFl...33g1905A. doi:10.1063/5.0055600. S2CID 233289904.
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em (2019-02-01). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". Journal of Computational Physics. 378: 686–707. Bibcode:2019JCoPh.378..686R. doi:10.1016/j.jcp.2018.10.045. ISSN 0021-9991. OSTI 1595805. S2CID 57379996.
Fu, Jinlong; Xiao, Dunhui; Fu, Rui; Li, Chenfeng; Zhu, Chuanhua; Arcucci, Rossella; Navon, Ionel M. (February 2023). "Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes". Computer Methods in Applied Mechanics and Engineering. 404 115771. Bibcode:2023CMAME.404k5771F. doi:10.1016/j.cma.2022.115771. S2CID 254397985.
Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (2020-02-28). "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations". Science. 367 (6481): 1026–1030. Bibcode:2020Sci...367.1026R. doi:10.1126/science.aaw4741. ISSN 0036-8075. PMC 7219083. PMID 32001523.
Jagtap, Ameya D.; Karniadakis, George Em (2020). "Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations". Communications in Computational Physics. 28 (5): 2002–2041. Bibcode:2020CCoPh..28.2002K. doi:10.4208/cicp.OA-2020-0164. OSTI 2282003. S2CID 229083388.
Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em (2020). "Conservative Physics-Informed Neural Networks on Discrete Domains for Conservation Laws: Applications to forward and inverse problems". Computer Methods in Applied Mechanics and Engineering. 365 113028. Bibcode:2020CMAME.365k3028J. doi:10.1016/j.cma.2020.113028. S2CID 216333271.
Schiassi, Enrico; Furfaro, Roberto; Leake, Carl; De Florio, Mario; Johnston, Hunter; Mortari, Daniele (October 2021). "Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations". Neurocomputing. 457: 334–356. Bibcode:2021Neurc.457..334S. doi:10.1016/j.neucom.2021.06.015. S2CID 236290147.
Schiassi, Enrico; De Florio, Mario; Ganapol, Barry D.; Picca, Paolo; Furfaro, Roberto (March 2022). "Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics". Annals of Nuclear Energy. 167 108833. Bibcode:2022AnNuE.16708833S. doi:10.1016/j.anucene.2021.108833. S2CID 244913655.
Schiassi, Enrico; D'Ambrosio, Andrea; Drozd, Kristofer; Curti, Fabio; Furfaro, Roberto (4 January 2022). "Physics-Informed Neural Networks for Optimal Planar Orbit Transfers". Journal of Spacecraft and Rockets. 59 (3): 834–849. Bibcode:2022JSpRo..59..834S. doi:10.2514/1.A35138. S2CID 245725265.
De Florio, Mario; Schiassi, Enrico; Ganapol, Barry D.; Furfaro, Roberto (April 2021). "Physics-informed neural networks for rarefied-gas dynamics: Thermal creep flow in the Bhatnagar–Gross–Krook approximation". Physics of Fluids. 33 (4): 047110. Bibcode:2021PhFl...33d7110D. doi:10.1063/5.0046181. S2CID 234852360.
Kashefi, Ali; Mukerji, Tapan (2022). "Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries". Journal of Computational Physics. 468 111510. arXiv:2202.05476. Bibcode:2022JCoPh.46811510K. doi:10.1016/j.jcp.2022.111510. S2CID 246823515.
Thanasutives, Pongpisit; Morita, Takashi; Numao, Masayuki; Fukui, Ken-ichi (2023-02-01). "Noise-aware physics-informed machine learning for robust PDE discovery". Machine Learning: Science and Technology. 4 (1): 015009. arXiv:2206.12901. Bibcode:2023MLS&T...4a5009T. doi:10.1088/2632-2153/acb1f0. ISSN 2632-2153.
Zhang, Enrui; Dao, Ming; Karniadakis, George Em; Suresh, Subra (2022-02-18). "Analyses of internal structures and defects in materials using physics-informed neural networks". Science Advances. 8 (7) eabk0644. Bibcode:2022SciA....8..644Z. doi:10.1126/sciadv.abk0644. ISSN 2375-2548. PMC 8849303. PMID 35171670.
Serebrennikova, Alexandra; Teubler, Raimund; Hoffellner, Lisa; Leitner, Erich; Hirn, Ulrich; Zojer, Karin (2022-12-01). "Transport of Organic Volatiles through Paper: Physics-Informed Neural Networks for Solving Inverse and Forward Problems". Transport in Porous Media. 145 (3): 589–612. Bibcode:2022TPMed.145..589S. doi:10.1007/s11242-022-01864-7. ISSN 1573-1634.
Jagtap, Ameya D.; Mao, Zhiping; Adams, Nikolaus; Karniadakis, George Em (October 2022). "Physics-informed neural networks for inverse problems in supersonic flows". Journal of Computational Physics. 466 111402. arXiv:2202.11821. Bibcode:2022JCoPh.46611402J. doi:10.1016/j.jcp.2022.111402. ISSN 0021-9991.
Yang, Liu; Meng, Xuhui; Karniadakis, George Em (January 2021). "B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data". Journal of Computational Physics. 425 109913. arXiv:2003.06097. Bibcode:2021JCoPh.42509913Y. doi:10.1016/j.jcp.2020.109913. ISSN 0021-9991.
Han, J.; Jentzen, A.; E, W. (2018). "Solving high-dimensional partial differential equations using deep learning". Proceedings of the National Academy of Sciences. 115 (34): 8505–8510. arXiv:1707.02568. Bibcode:2018PNAS..115.8505H. doi:10.1073/pnas.1718942115. PMC 6112690. PMID 30082389.
Rohrhofer, Franz M.; Posch, Stefan; Gößnitzer, Clemens; Geiger, Bernhard C. (2023). "Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks". IEEE Access. 11: 86252–86261. arXiv:2105.00862. Bibcode:2023IEEEA..1186252R. doi:10.1109/ACCESS.2023.3302892. ISSN 2169-3536.

arxiv.org (Global: 49^th place; English: 31^st place)

Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em (2017-11-28). "Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations". arXiv:1711.10561 [cs.AI].
Torabi Rad, M.; Viardin, A.; Schmitz, G.J.; Apel, M. (2020-03-01). "Theory-training deep neural networks for an alloy solidification benchmark problem". Computational Materials Science. 18 109687. arXiv:1912.09800. doi:10.1016/j.commatsci.2020.109687. ISSN 0893-6080.
Arzani, Amirhossein; Dawson, Scott T. M. (2021). "Data-driven cardiovascular flow modelling: examples and opportunities". Journal of the Royal Society Interface. 18 (175) 20200802. arXiv:2010.00131. doi:10.1098/rsif.2020.0802. PMC 8086862. PMID 33561376.
Arzani, Amirhossein; Wang, Jian-Xun; D'Souza, Roshan M. (2021-06-07). "Uncovering near-wall blood flow from sparse data with physics-informed neural networks". Physics of Fluids. 33 (7): 071905. arXiv:2104.08249. Bibcode:2021PhFl...33g1905A. doi:10.1063/5.0055600. S2CID 233289904.
Markidis, Stefano (2021-03-11). "Physics-Informed Deep-Learning for Scientific Computing". arXiv:2103.09655 [math.NA].
Baydin, Atilim Gunes; Pearlmutter, Barak A.; Radul, Alexey Andreyevich; Siskind, Jeffrey Mark (2018-02-05). "Automatic differentiation in machine learning: a survey". arXiv:1502.05767 [cs.SC].
Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (2018-08-13). "Hidden Fluid Mechanics: A Navier–Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data". arXiv:1808.04327 [cs.CE].
Doumèche, Nathan; Biau, Gérard; Boyer, Claire (2025-08-01). "On the convergence of PINNs". Bernoulli. 31 (3). arXiv:2305.01240. doi:10.3150/24-bej1799. ISSN 1350-7265.
Mishra, Siddhartha; Molinaro, Roberto (2021-04-01). "Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs". arXiv:2007.01138 [math.NA].
Ryck, Tim De; Jagtap, Ameya D.; Mishra, Siddhartha (2022). "Error estimates for physics informed neural networks approximating the Navier–Stokes equations". arXiv:2203.09346 [math.NA].
Dwivedi, Vikas; Parashar, Nishant; Srinivasan, Balaji (2021-01-08). "Distributed learning machines for solving forward and inverse problems in partial differential equations". Neurocomputing. 420: 299–316. arXiv:1907.08967. doi:10.1016/j.neucom.2020.09.006. ISSN 0925-2312. S2CID 225014697.
Rout, Siddharth (2019). "Numerical Approximation in CFD Problems Using Physics Informed Machine Learning". arXiv:2111.02987 [cs.LG]. Master's Thesis, Indian Institute of Technology Madras, July 2019.
Kashefi, Ali; Mukerji, Tapan (2022). "Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries". Journal of Computational Physics. 468 111510. arXiv:2202.05476. Bibcode:2022JCoPh.46811510K. doi:10.1016/j.jcp.2022.111510. S2CID 246823515.
Qi, Charles; Su, Hao; Mo, Kaichun; Guibas, Leonidas (2017). "Pointnet: Deep learning on point sets for 3d classification and segmentation" (PDF). Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition: 652–660. arXiv:1612.00593.
Kashefi, Ali; Mukerji, Tapan (2023). "Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity". arXiv:2303.13634 [cs.LG].
Thanasutives, Pongpisit; Morita, Takashi; Numao, Masayuki; Fukui, Ken-ichi (2023-02-01). "Noise-aware physics-informed machine learning for robust PDE discovery". Machine Learning: Science and Technology. 4 (1): 015009. arXiv:2206.12901. Bibcode:2023MLS&T...4a5009T. doi:10.1088/2632-2153/acb1f0. ISSN 2632-2153.
Jagtap, Ameya D.; Mao, Zhiping; Adams, Nikolaus; Karniadakis, George Em (October 2022). "Physics-informed neural networks for inverse problems in supersonic flows". Journal of Computational Physics. 466 111402. arXiv:2202.11821. Bibcode:2022JCoPh.46611402J. doi:10.1016/j.jcp.2022.111402. ISSN 0021-9991.
Yang, Liu; Meng, Xuhui; Karniadakis, George Em (January 2021). "B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data". Journal of Computational Physics. 425 109913. arXiv:2003.06097. Bibcode:2021JCoPh.42509913Y. doi:10.1016/j.jcp.2020.109913. ISSN 0021-9991.
Vicens Figueres, Júlia; Vanderhaeghen, Juliette; Bragone, Federica; Morozovska, Kateryna; Shukla, Khemraj (2025). "$PINN - a Domain Decomposition Method for Bayesian Physics-Informed Neural Networks". arXiv:2504.19013v1 [cs.LG].
Bragone, Federica; Morozovska, Kateryna; Laneryd, Tor; Shukla, Khemraj; Markidis, Stefano (2025). "Discovering Partially Known Ordinary Differential Equations: a Case Study on the Chemical Kinetics of Cellulose Degradation". arXiv:2504.03484 [cs.LG].
Han, J.; Jentzen, A.; E, W. (2018). "Solving high-dimensional partial differential equations using deep learning". Proceedings of the National Academy of Sciences. 115 (34): 8505–8510. arXiv:1707.02568. Bibcode:2018PNAS..115.8505H. doi:10.1073/pnas.1718942115. PMC 6112690. PMID 30082389.
Mojgani, Rambod; Balajewicz, Maciej; Hassanzadeh, Pedram (February 2023). "Kolmogorov n–width and Lagrangian physics-informed neural networks: A causality-conforming manifold for convection-dominated PDEs". Computer Methods in Applied Mechanics and Engineering. 404 115810. arXiv:2205.02902. doi:10.1016/j.cma.2022.115810.
Eric Aislan Antonelo; Camponogara, Eduardo; Laio Oriel Seman; Eduardo Rehbein de Souza; Jordanou, Jean P.; Hubner, Jomi F. (2024). "Physics-informed neural nets for control of dynamical systems". Neurocomputing. 579 127419. arXiv:2104.02556. doi:10.1016/j.neucom.2024.127419.
Rohrhofer, Franz M.; Posch, Stefan; Gößnitzer, Clemens; Geiger, Bernhard C. (2023). "Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks". IEEE Access. 11: 86252–86261. arXiv:2105.00862. Bibcode:2023IEEEA..1186252R. doi:10.1109/ACCESS.2023.3302892. ISSN 2169-3536.
Wang, Sifan; Teng, Yujun; Perdikaris, Paris (2020-01-13). "Understanding and mitigating gradient pathologies in physics-informed neural networks". arXiv:2001.04536 [cs.LG].

creativecommons.org (Global: 580^th place; English: 287^th place)

Mouratidou, Aliki D.; Daraki, Maria-Styliani; Drosopoulos, Georgios A.; Foutsitzi, Georgia; Larbi, Walid; Deü, Jean-Francois; Ohayon, Roger; Stavroulakis, Georgios E. (5 February 2026). "Physics-informed neural networks for shunted piezoelectric systems". Acta Mechanica. doi:10.1007/s00707-025-04619-9. ISSN 1619-6937. Retrieved 4 March 2026. This article incorporates text from this source, which is available under the CC BY 4.0 license.

doi.org (Global: 2^nd place; English: 2^nd place)

Torabi Rad, M.; Viardin, A.; Schmitz, G.J.; Apel, M. (2020-03-01). "Theory-training deep neural networks for an alloy solidification benchmark problem". Computational Materials Science. 18 109687. arXiv:1912.09800. doi:10.1016/j.commatsci.2020.109687. ISSN 0893-6080.
Hornik, Kurt; Tinchcombe, Maxwell; White, Halbert (1989-01-01). "Multilayer feedforward networks are universal approximators". Neural Networks. 2 (5): 359–366. doi:10.1016/0893-6080(89)90020-8. ISSN 0893-6080. S2CID 2757547.
Arzani, Amirhossein; Dawson, Scott T. M. (2021). "Data-driven cardiovascular flow modelling: examples and opportunities". Journal of the Royal Society Interface. 18 (175) 20200802. arXiv:2010.00131. doi:10.1098/rsif.2020.0802. PMC 8086862. PMID 33561376.
Arzani, Amirhossein; Wang, Jian-Xun; D'Souza, Roshan M. (2021-06-07). "Uncovering near-wall blood flow from sparse data with physics-informed neural networks". Physics of Fluids. 33 (7): 071905. arXiv:2104.08249. Bibcode:2021PhFl...33g1905A. doi:10.1063/5.0055600. S2CID 233289904.
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em (2019-02-01). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". Journal of Computational Physics. 378: 686–707. Bibcode:2019JCoPh.378..686R. doi:10.1016/j.jcp.2018.10.045. ISSN 0021-9991. OSTI 1595805. S2CID 57379996.
Doumèche, Nathan; Biau, Gérard; Boyer, Claire (2025-08-01). "On the convergence of PINNs". Bernoulli. 31 (3). arXiv:2305.01240. doi:10.3150/24-bej1799. ISSN 1350-7265.
Fu, Jinlong; Xiao, Dunhui; Fu, Rui; Li, Chenfeng; Zhu, Chuanhua; Arcucci, Rossella; Navon, Ionel M. (February 2023). "Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes". Computer Methods in Applied Mechanics and Engineering. 404 115771. Bibcode:2023CMAME.404k5771F. doi:10.1016/j.cma.2022.115771. S2CID 254397985.
Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (2020-02-28). "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations". Science. 367 (6481): 1026–1030. Bibcode:2020Sci...367.1026R. doi:10.1126/science.aaw4741. ISSN 0036-8075. PMC 7219083. PMID 32001523.
Dwivedi, Vikas; Parashar, Nishant; Srinivasan, Balaji (2021-01-08). "Distributed learning machines for solving forward and inverse problems in partial differential equations". Neurocomputing. 420: 299–316. arXiv:1907.08967. doi:10.1016/j.neucom.2020.09.006. ISSN 0925-2312. S2CID 225014697.
Jagtap, Ameya D.; Karniadakis, George Em (2020). "Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations". Communications in Computational Physics. 28 (5): 2002–2041. Bibcode:2020CCoPh..28.2002K. doi:10.4208/cicp.OA-2020-0164. OSTI 2282003. S2CID 229083388.
Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em (2020). "Conservative Physics-Informed Neural Networks on Discrete Domains for Conservation Laws: Applications to forward and inverse problems". Computer Methods in Applied Mechanics and Engineering. 365 113028. Bibcode:2020CMAME.365k3028J. doi:10.1016/j.cma.2020.113028. S2CID 216333271.
Leake, Carl; Mortari, Daniele (March 2020). "Deep Theory of Functional Connections: A New Method for Estimating the Solutions of Partial Differential Equations". Machine Learning and Knowledge Extraction. 2 (1): 37–55. doi:10.3390/make2010004. ISSN 2504-4990. PMC 7259480. PMID 32478283.
Leake, Carl; Mortari, Daniele (12 March 2020). "Deep Theory of Functional Connections: A New Method for Estimating the Solutions of Partial Differential Equations". Machine Learning and Knowledge Extraction. 2 (1): 37–55. doi:10.3390/make2010004. PMC 7259480. PMID 32478283.
Schiassi, Enrico; Furfaro, Roberto; Leake, Carl; De Florio, Mario; Johnston, Hunter; Mortari, Daniele (October 2021). "Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations". Neurocomputing. 457: 334–356. Bibcode:2021Neurc.457..334S. doi:10.1016/j.neucom.2021.06.015. S2CID 236290147.
Schiassi, Enrico; De Florio, Mario; Ganapol, Barry D.; Picca, Paolo; Furfaro, Roberto (March 2022). "Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics". Annals of Nuclear Energy. 167 108833. Bibcode:2022AnNuE.16708833S. doi:10.1016/j.anucene.2021.108833. S2CID 244913655.
Schiassi, Enrico; D'Ambrosio, Andrea; Drozd, Kristofer; Curti, Fabio; Furfaro, Roberto (4 January 2022). "Physics-Informed Neural Networks for Optimal Planar Orbit Transfers". Journal of Spacecraft and Rockets. 59 (3): 834–849. Bibcode:2022JSpRo..59..834S. doi:10.2514/1.A35138. S2CID 245725265.
De Florio, Mario; Schiassi, Enrico; Ganapol, Barry D.; Furfaro, Roberto (April 2021). "Physics-informed neural networks for rarefied-gas dynamics: Thermal creep flow in the Bhatnagar–Gross–Krook approximation". Physics of Fluids. 33 (4): 047110. Bibcode:2021PhFl...33d7110D. doi:10.1063/5.0046181. S2CID 234852360.
Kashefi, Ali; Mukerji, Tapan (2022). "Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries". Journal of Computational Physics. 468 111510. arXiv:2202.05476. Bibcode:2022JCoPh.46811510K. doi:10.1016/j.jcp.2022.111510. S2CID 246823515.
Thanasutives, Pongpisit; Morita, Takashi; Numao, Masayuki; Fukui, Ken-ichi (2023-02-01). "Noise-aware physics-informed machine learning for robust PDE discovery". Machine Learning: Science and Technology. 4 (1): 015009. arXiv:2206.12901. Bibcode:2023MLS&T...4a5009T. doi:10.1088/2632-2153/acb1f0. ISSN 2632-2153.
Zhang, Enrui; Dao, Ming; Karniadakis, George Em; Suresh, Subra (2022-02-18). "Analyses of internal structures and defects in materials using physics-informed neural networks". Science Advances. 8 (7) eabk0644. Bibcode:2022SciA....8..644Z. doi:10.1126/sciadv.abk0644. ISSN 2375-2548. PMC 8849303. PMID 35171670.
Serebrennikova, Alexandra; Teubler, Raimund; Hoffellner, Lisa; Leitner, Erich; Hirn, Ulrich; Zojer, Karin (2022-12-01). "Transport of Organic Volatiles through Paper: Physics-Informed Neural Networks for Solving Inverse and Forward Problems". Transport in Porous Media. 145 (3): 589–612. Bibcode:2022TPMed.145..589S. doi:10.1007/s11242-022-01864-7. ISSN 1573-1634.
Abbasi, Jassem; Andersen, Pål Østebø (2024-01-01). "Application of Physics-Informed Neural Networks for Estimation of Saturation Functions from Countercurrent Spontaneous Imbibition Tests". SPE Journal. 29 (4): 1710–1729. doi:10.2118/218402-PA. ISSN 1086-055X.
Jagtap, Ameya D.; Mao, Zhiping; Adams, Nikolaus; Karniadakis, George Em (October 2022). "Physics-informed neural networks for inverse problems in supersonic flows". Journal of Computational Physics. 466 111402. arXiv:2202.11821. Bibcode:2022JCoPh.46611402J. doi:10.1016/j.jcp.2022.111402. ISSN 0021-9991.
Yang, Liu; Meng, Xuhui; Karniadakis, George Em (January 2021). "B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data". Journal of Computational Physics. 425 109913. arXiv:2003.06097. Bibcode:2021JCoPh.42509913Y. doi:10.1016/j.jcp.2020.109913. ISSN 0021-9991.
Mouratidou, Aliki D.; Daraki, Maria-Styliani; Drosopoulos, Georgios A.; Foutsitzi, Georgia; Larbi, Walid; Deü, Jean-Francois; Ohayon, Roger; Stavroulakis, Georgios E. (5 February 2026). "Physics-informed neural networks for shunted piezoelectric systems". Acta Mechanica. doi:10.1007/s00707-025-04619-9. ISSN 1619-6937. Retrieved 4 March 2026. This article incorporates text from this source, which is available under the CC BY 4.0 license.
Muradova, Aliki D.; Stavroulakis, Georgios E. (2021-12-30). "Physics-Informed Neural Networks for Elastic Plate Problems with Bending and Winkler-Type Contact Effects". Journal of the Serbian Society for Computational Mechanics. 15 (2): 46–55. doi:10.24874/jsscm.2021.15.02.05.
Stavroulakis, G.E., Mouratidou, A.D., Drosopoulos, G.A. (2025) Physics-Informed Neural Networks. In: Pardalos, P.M., Prokopyev, O.A. (eds) Encyclopedia of Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-54621-2_907-1
Mouratidou, A.D., Daraki, MS., Drosopoulos, G.A. et al. Physics-informed neural networks for shunted piezoelectric systems. Acta Mechanica (2026). https://doi.org/10.1007/s00707-025-04619-9
Han, J.; Jentzen, A.; E, W. (2018). "Solving high-dimensional partial differential equations using deep learning". Proceedings of the National Academy of Sciences. 115 (34): 8505–8510. arXiv:1707.02568. Bibcode:2018PNAS..115.8505H. doi:10.1073/pnas.1718942115. PMC 6112690. PMID 30082389.
Lagergren JH, Nardini JT, Baker RE, Simpson MJ, Flores KB (2020). "Biologically-informed neural networks guide mechanistic modeling from sparse experimental data." PLoS Comput Biol 16(12): e1008462. https://doi.org/10.1371/journal.pcbi.1008462
Nardini JT (2024). "Forecasting and Predicting Stochastic Agent-Based Model Data with Biologically-Informed Neural Networks." Bull Math Biol 86, 130. https://doi.org/10.1007/s11538-024-01357-2
Mojgani, Rambod; Balajewicz, Maciej; Hassanzadeh, Pedram (February 2023). "Kolmogorov n–width and Lagrangian physics-informed neural networks: A causality-conforming manifold for convection-dominated PDEs". Computer Methods in Applied Mechanics and Engineering. 404 115810. arXiv:2205.02902. doi:10.1016/j.cma.2022.115810.
Eric Aislan Antonelo; Camponogara, Eduardo; Laio Oriel Seman; Eduardo Rehbein de Souza; Jordanou, Jean P.; Hubner, Jomi F. (2024). "Physics-informed neural nets for control of dynamical systems". Neurocomputing. 579 127419. arXiv:2104.02556. doi:10.1016/j.neucom.2024.127419.
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ieee.org (Global: 912^th place; English: 722^nd place)

ieeexplore.ieee.org

Welin Odeback, Oliver; Bragone, Federica; Laneryd, Tor; Luvisotto, Michele; Morozovska, Kateryna (2022-12-12). Physics-Informed Neural Networks for prediction of transformer's temperature distribution. 2022 21st IEEE International Conference on Machine Learning and Applications (ICMLA). Nassau, Bahamas: IEEE. pp. 1579–1586.

iop.org (Global: 1,046^th place; English: 1,608^th place)

iopscience.iop.org

Thanasutives, Pongpisit; Morita, Takashi; Numao, Masayuki; Fukui, Ken-ichi (2023-02-01). "Noise-aware physics-informed machine learning for robust PDE discovery". Machine Learning: Science and Technology. 4 (1): 015009. arXiv:2206.12901. Bibcode:2023MLS&T...4a5009T. doi:10.1088/2632-2153/acb1f0. ISSN 2632-2153.

kg.ac.rs (Global: low place; English: low place)

sscm.kg.ac.rs

Muradova, Aliki D.; Stavroulakis, Georgios E. (2021-12-30). "Physics-Informed Neural Networks for Elastic Plate Problems with Bending and Winkler-Type Contact Effects". Journal of the Serbian Society for Computational Mechanics. 15 (2): 46–55. doi:10.24874/jsscm.2021.15.02.05.

nih.gov (Global: 5^th place; English: 5^th place)

ncbi.nlm.nih.gov

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pubmed.ncbi.nlm.nih.gov

Arzani, Amirhossein; Dawson, Scott T. M. (2021). "Data-driven cardiovascular flow modelling: examples and opportunities". Journal of the Royal Society Interface. 18 (175) 20200802. arXiv:2010.00131. doi:10.1098/rsif.2020.0802. PMC 8086862. PMID 33561376.
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onepetro.org (Global: low place; English: low place)

Abbasi, Jassem; Andersen, Pål Østebø (2024-01-01). "Application of Physics-Informed Neural Networks for Estimation of Saturation Functions from Countercurrent Spontaneous Imbibition Tests". SPE Journal. 29 (4): 1710–1729. doi:10.2118/218402-PA. ISSN 1086-055X.

openreview.net (Global: low place; English: low place)

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optica.org (Global: low place; English: 9,523^rd place)

opg.optica.org

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osti.gov (Global: 2,098^th place; English: 1,146^th place)

Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em (2019-02-01). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". Journal of Computational Physics. 378: 686–707. Bibcode:2019JCoPh.378..686R. doi:10.1016/j.jcp.2018.10.045. ISSN 0021-9991. OSTI 1595805. S2CID 57379996.
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projecteuclid.org (Global: 4,781^st place; English: 3,117^th place)

Doumèche, Nathan; Biau, Gérard; Boyer, Claire (2025-08-01). "On the convergence of PINNs". Bernoulli. 31 (3). arXiv:2305.01240. doi:10.3150/24-bej1799. ISSN 1350-7265.

sciencedirect.com (Global: 137^th place; English: 146^th place)

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semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Hornik, Kurt; Tinchcombe, Maxwell; White, Halbert (1989-01-01). "Multilayer feedforward networks are universal approximators". Neural Networks. 2 (5): 359–366. doi:10.1016/0893-6080(89)90020-8. ISSN 0893-6080. S2CID 2757547.
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Fu, Jinlong; Xiao, Dunhui; Fu, Rui; Li, Chenfeng; Zhu, Chuanhua; Arcucci, Rossella; Navon, Ionel M. (February 2023). "Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes". Computer Methods in Applied Mechanics and Engineering. 404 115771. Bibcode:2023CMAME.404k5771F. doi:10.1016/j.cma.2022.115771. S2CID 254397985.
Dwivedi, Vikas; Parashar, Nishant; Srinivasan, Balaji (2021-01-08). "Distributed learning machines for solving forward and inverse problems in partial differential equations". Neurocomputing. 420: 299–316. arXiv:1907.08967. doi:10.1016/j.neucom.2020.09.006. ISSN 0925-2312. S2CID 225014697.
Jagtap, Ameya D.; Karniadakis, George Em (2020). "Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations". Communications in Computational Physics. 28 (5): 2002–2041. Bibcode:2020CCoPh..28.2002K. doi:10.4208/cicp.OA-2020-0164. OSTI 2282003. S2CID 229083388.
Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em (2020). "Conservative Physics-Informed Neural Networks on Discrete Domains for Conservation Laws: Applications to forward and inverse problems". Computer Methods in Applied Mechanics and Engineering. 365 113028. Bibcode:2020CMAME.365k3028J. doi:10.1016/j.cma.2020.113028. S2CID 216333271.
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springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Mouratidou, Aliki D.; Daraki, Maria-Styliani; Drosopoulos, Georgios A.; Foutsitzi, Georgia; Larbi, Walid; Deü, Jean-Francois; Ohayon, Roger; Stavroulakis, Georgios E. (5 February 2026). "Physics-informed neural networks for shunted piezoelectric systems". Acta Mechanica. doi:10.1007/s00707-025-04619-9. ISSN 1619-6937. Retrieved 4 March 2026. This article incorporates text from this source, which is available under the CC BY 4.0 license.

swan.ac.uk (Global: low place; English: low place)

cronfa.swan.ac.uk

Fu, Jinlong; Xiao, Dunhui; Fu, Rui; Li, Chenfeng; Zhu, Chuanhua; Arcucci, Rossella; Navon, Ionel M. (February 2023). "Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes". Computer Methods in Applied Mechanics and Engineering. 404 115771. Bibcode:2023CMAME.404k5771F. doi:10.1016/j.cma.2022.115771. S2CID 254397985.

thecvf.com (Global: low place; English: low place)

openaccess.thecvf.com

Qi, Charles; Su, Hao; Mo, Kaichun; Guibas, Leonidas (2017). "Pointnet: Deep learning on point sets for 3d classification and segmentation" (PDF). Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition: 652–660. arXiv:1612.00593.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Torabi Rad, M.; Viardin, A.; Schmitz, G.J.; Apel, M. (2020-03-01). "Theory-training deep neural networks for an alloy solidification benchmark problem". Computational Materials Science. 18 109687. arXiv:1912.09800. doi:10.1016/j.commatsci.2020.109687. ISSN 0893-6080.
Hornik, Kurt; Tinchcombe, Maxwell; White, Halbert (1989-01-01). "Multilayer feedforward networks are universal approximators". Neural Networks. 2 (5): 359–366. doi:10.1016/0893-6080(89)90020-8. ISSN 0893-6080. S2CID 2757547.
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em (2019-02-01). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". Journal of Computational Physics. 378: 686–707. Bibcode:2019JCoPh.378..686R. doi:10.1016/j.jcp.2018.10.045. ISSN 0021-9991. OSTI 1595805. S2CID 57379996.
Doumèche, Nathan; Biau, Gérard; Boyer, Claire (2025-08-01). "On the convergence of PINNs". Bernoulli. 31 (3). arXiv:2305.01240. doi:10.3150/24-bej1799. ISSN 1350-7265.
Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (2020-02-28). "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations". Science. 367 (6481): 1026–1030. Bibcode:2020Sci...367.1026R. doi:10.1126/science.aaw4741. ISSN 0036-8075. PMC 7219083. PMID 32001523.
Dwivedi, Vikas; Parashar, Nishant; Srinivasan, Balaji (2021-01-08). "Distributed learning machines for solving forward and inverse problems in partial differential equations". Neurocomputing. 420: 299–316. arXiv:1907.08967. doi:10.1016/j.neucom.2020.09.006. ISSN 0925-2312. S2CID 225014697.
Leake, Carl; Mortari, Daniele (March 2020). "Deep Theory of Functional Connections: A New Method for Estimating the Solutions of Partial Differential Equations". Machine Learning and Knowledge Extraction. 2 (1): 37–55. doi:10.3390/make2010004. ISSN 2504-4990. PMC 7259480. PMID 32478283.
Thanasutives, Pongpisit; Morita, Takashi; Numao, Masayuki; Fukui, Ken-ichi (2023-02-01). "Noise-aware physics-informed machine learning for robust PDE discovery". Machine Learning: Science and Technology. 4 (1): 015009. arXiv:2206.12901. Bibcode:2023MLS&T...4a5009T. doi:10.1088/2632-2153/acb1f0. ISSN 2632-2153.
Zhang, Enrui; Dao, Ming; Karniadakis, George Em; Suresh, Subra (2022-02-18). "Analyses of internal structures and defects in materials using physics-informed neural networks". Science Advances. 8 (7) eabk0644. Bibcode:2022SciA....8..644Z. doi:10.1126/sciadv.abk0644. ISSN 2375-2548. PMC 8849303. PMID 35171670.
Serebrennikova, Alexandra; Teubler, Raimund; Hoffellner, Lisa; Leitner, Erich; Hirn, Ulrich; Zojer, Karin (2022-12-01). "Transport of Organic Volatiles through Paper: Physics-Informed Neural Networks for Solving Inverse and Forward Problems". Transport in Porous Media. 145 (3): 589–612. Bibcode:2022TPMed.145..589S. doi:10.1007/s11242-022-01864-7. ISSN 1573-1634.
Abbasi, Jassem; Andersen, Pål Østebø (2024-01-01). "Application of Physics-Informed Neural Networks for Estimation of Saturation Functions from Countercurrent Spontaneous Imbibition Tests". SPE Journal. 29 (4): 1710–1729. doi:10.2118/218402-PA. ISSN 1086-055X.
Jagtap, Ameya D.; Mao, Zhiping; Adams, Nikolaus; Karniadakis, George Em (October 2022). "Physics-informed neural networks for inverse problems in supersonic flows". Journal of Computational Physics. 466 111402. arXiv:2202.11821. Bibcode:2022JCoPh.46611402J. doi:10.1016/j.jcp.2022.111402. ISSN 0021-9991.
Yang, Liu; Meng, Xuhui; Karniadakis, George Em (January 2021). "B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data". Journal of Computational Physics. 425 109913. arXiv:2003.06097. Bibcode:2021JCoPh.42509913Y. doi:10.1016/j.jcp.2020.109913. ISSN 0021-9991.
Mouratidou, Aliki D.; Daraki, Maria-Styliani; Drosopoulos, Georgios A.; Foutsitzi, Georgia; Larbi, Walid; Deü, Jean-Francois; Ohayon, Roger; Stavroulakis, Georgios E. (5 February 2026). "Physics-informed neural networks for shunted piezoelectric systems". Acta Mechanica. doi:10.1007/s00707-025-04619-9. ISSN 1619-6937. Retrieved 4 March 2026. This article incorporates text from this source, which is available under the CC BY 4.0 license.
Rohrhofer, Franz M.; Posch, Stefan; Gößnitzer, Clemens; Geiger, Bernhard C. (2023). "Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks". IEEE Access. 11: 86252–86261. arXiv:2105.00862. Bibcode:2023IEEEA..1186252R. doi:10.1109/ACCESS.2023.3302892. ISSN 2169-3536.
Rohrhofer, Franz M.; Posch, Stefan; Gößnitzer, Clemens; Geiger, Bernhard C. (2022-10-20). "On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks". Transactions on Machine Learning Research. ISSN 2835-8856.

Physics-informed neural networks (English Wikipedia)

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