Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Physics-informed neural network for engineers: a review from an implementation aspect

  • Review Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In order to offer guidelines for physics-informed neural network (PINN) implementation, this study presents a comprehensive review of PINN, an emerging field at the intersection of deep learning and computational physics. PINN offers a novel approach to solve physics problems by leveraging the flexibility and scalability of neural networks, even with small or no data. First, a general description of different physics problem types and target tasks addressable with PINN was provided. A generic PINN architecture was described in detail using a component-wise approach, with components ranging from collocation points to optimization methods. Then, we surveyed studies that sought to improve upon each of these components. To offer practical insights, we highlighted studies that focused on key issues of PINN implementation and showcased three practical applications. Lastly, a summary and potential research directions were provided to offer guidelines for reliable and customized PINN implementations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Find the latest articles, discoveries, and news in related topics.

References

  1. S. W. Kim, I. Kim and J. Lee, Seungchul knowledge integration into deep learning in dynamical systems: an overview and taxonomy, Journal of Mechanical Science and Technology, 35 (2021) 1331–1342.

    Article  Google Scholar 

  2. M. P. Raissi and G. E. P. Karniadakis, Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics, 378 (2019) 686–707.

    Article  MathSciNet  Google Scholar 

  3. S. Cai et al., Physics-informed neural networks (PINNs) for fluid mechanics: a review, Acta Mechanica Sinica, 37 (12) (2021) 1727–1738.

    Article  MathSciNet  Google Scholar 

  4. S. Cai et al., Physics-informed neural networks for heat transfer problems, J. Heat Transfer, 143 (6) (2021) 060801.

    Article  Google Scholar 

  5. G. E. Karniadakis et al., Physics-informed machine learning, Nature Reviews Physics, 3 (6) (2021) 422–440.

    Article  Google Scholar 

  6. S. Cuomo et al., Scientific Machine learning through physics-informed neural networks: where we are and what’s next, Journal of Scientific Computing, 92 (3) (2022) 88.

    Article  MathSciNet  Google Scholar 

  7. S. Das and S. Tesfamariam, State-of-the-art review of design of experiments for physics-informed deep learning, arXiv.2202.06416 (2022) DOI: https://doi.org/10.48550/arXiv.2202.06416.

  8. X. Mou, Q. Fang and S. Li, A hybrid neural network and data sampling solver for forward and backward modiied diffusion equations, Research Square (2022) https://www.research-square.com/article/rs-2059725/v1 (Preprint).

  9. L. Lu et al., DeepXDE: a deep learning library for solving differential equations, SIAM Review, 63 (1) (2021) 208–228.

    Article  MathSciNet  Google Scholar 

  10. J. M. Hanna et al., Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks, Computer Methods in Applied Mechanics and Engineering, 396 (2022) 115100.

    Article  MathSciNet  Google Scholar 

  11. C. Wu et al., A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks, Computer Methods in Applied Mechanics and Engineering, 403 (2023) 115671.

    Article  MathSciNet  Google Scholar 

  12. W. Peng et al., RANG: a residual-based adaptive node generation method for physics-informed neural networks, arXiv:2205.01051 (2022) DOI: https://doi.org/10.48550/arXiv.2205.01051.

  13. S. Subramanian et al., Adaptive self-supervision algorithms for physics-informed neural networks, arXiv:2207.04084 (2022) DOI: https://doi.org/10.48550/arXiv.2207.04084.

  14. A. D. Jagtap, K. Kawaguchi and G. E. Karniadakis, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics, 404 (2020) 109136.

    Article  MathSciNet  Google Scholar 

  15. A. D. Jagtap, K. Kawaguchi and G. Em Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476 (2239) (2020) 20200334.

    Article  MathSciNet  Google Scholar 

  16. R. Gnanasambandam et al., Self-scalable tanh (stan): faster convergence and better generalization in physics-informed neural networks, arXiv:2204.12589 (2022) DOI: https://doi.org/10.48550/arXiv.2204.12589.

  17. J. Abbasi and P. Ø. Andersen, Physical activation functions (pafs): an approach for more efficient induction of physics into physics-informed neural networks (PINNs), arXiv:2205.14630 (2022) DOI: https://doi.org/10.48550/arXiv.2205.14630.

  18. W. Peng et al., Accelerating physics-informed neural network training with prior dictionaries, arXiv:2004.08151 (2020) DOI: https://doi.org/10.48550/arXiv.2004.08151.

  19. K. He et al., Deep residual learning for image recognition, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA (2016).

  20. C. Cheng and G.-T. Zhang, Deep learning method based on physics informed neural network with resnet block for solving fluid flow problems, Water, 13 (2021) 423, DOI: https://doi.org/10.3390/w13040423.

    Article  Google Scholar 

  21. C. Moya and G. Lin, DAE-PINN: a physics-informed neural network model for simulating differential algebraic equations with application to power networks, Neural Computing and Applications, 35 (5) (2023) 3789–3804.

    Article  Google Scholar 

  22. V. Dwivedi and B. Srinivasan, Physics informed extreme learning machine (PIELM)–a rapid method for the numerical solution of partial differential equations, Neurocomputing, 391 (2020) 96–118.

    Article  Google Scholar 

  23. E. Schiassi et al., Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations, Neurocomputing, 457 (2021) 334–356.

    Article  Google Scholar 

  24. A. A. Ramabathiran and P. Ramachandran, SPINN: sparse, physics-based, and partially interpretable neural networks for PDEs, Journal of Computational Physics, 445 (2021) 110600.

    Article  MathSciNet  Google Scholar 

  25. H. Gao, L. Sun and J.-X. Wang, PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain, Journal of Computational Physics, 428 (2021) 110079.

    Article  MathSciNet  Google Scholar 

  26. L. Sun et al., Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data, Computer Methods in Applied Mechanics and Engineering, 361 (2020) 112732.

    Article  MathSciNet  Google Scholar 

  27. L. Lu et al., Physics-informed neural networks with hard constraints for inverse design, SIAM Journal on Scientific Computing, 43 (6) (2021) B1105–B1132.

    Article  MathSciNet  Google Scholar 

  28. R. Gong and Z. Tang, Further investigation of convolutional neural networks applied in computational electromagnetism under physics-informed consideration, IET Electr. Power Appl., 16 (6) (2022) 653–674.

    Article  Google Scholar 

  29. X. Zhao et al., Physics-informed convolutional neural networks for temperature field prediction of heat source layout without labeled data, Engineering Applications of Artificial Intelligence, 117 (2023) 105516.

    Article  Google Scholar 

  30. Y. Yang and P. Perdikaris, Adversarial uncertainty quantification in physics-informed neural networks, Journal of Computational Physics, 394 (2019) 136–152.

    Article  MathSciNet  Google Scholar 

  31. L. Yang et al., Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs, 2019 IEEE/ACM Third Workshop on Deep Learning on Supercomputers (DLS), Penver, CO, USA (2019).

  32. A. Daw, M. Maruf and A. Karpatne, PID-GAN: a GAN framework based on a physics-informed discriminator for uncertainty quantification with physics, Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, Association for Computing Machinery, Virtual Event, Singapore (2021) 237–247.

  33. W. Zhong and H. Meidani, PI-VAE: physics-informed variational auto-encoder for stochastic differential equations, Computer Methods in Applied Mechanics and Engineering, 403 (2023) 115664.

    Article  MathSciNet  Google Scholar 

  34. Y. A. Yucesan and F. A. C. Viana, A hybrid physics-informed neural network for main bearing fatigue prognosis under grease quality variation, Mechanical Systems and Signal Processingy, 171 (2022) 108875.

    Article  Google Scholar 

  35. R. Zhang, Y. Liu and H. Sun, Physics-informed multi-LSTM networks for metamodeling of nonlinear structures, Computer Methods in Applied Mechanics and Engineering, 369 (2020) 113226.

    Article  MathSciNet  Google Scholar 

  36. P. Ren et al., PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs, Computer Methods in Applied Mechanics and Engineering, 389 (2022) 114399.

    Article  MathSciNet  Google Scholar 

  37. L. Lu et al., Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, Nature Machine Intelligence, 3 (3) (2021) 218–229.

    Article  Google Scholar 

  38. K. Hornik and M. W. Stinchcombe, Halbert, multilayer feedforward networks are universal approximators, Neural Networks, 2 (1989) 359–366.

    Article  Google Scholar 

  39. S. Wang, H. Wang and P. Perdikaris, Learning the solution operator of parametric partial differential equations with physics-informed DeepONets, Science Advances, 7 (40) (2021) eabi8605.

    Article  Google Scholar 

  40. S. Cai et al., DeepM&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks, Journal of Computational Physics, 436 (2021) 110296.

    Article  MathSciNet  Google Scholar 

  41. L. Yang, X. Meng and G. E. Karniadakis, B-PINNs: bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data, Journal of Computational Physics, 425 (2021) 109913.

    Article  MathSciNet  Google Scholar 

  42. J. Li, J. Chen and B. Li, Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation, Nonlinear Dynamics, 107 (1) (2022) 781–792.

    Article  Google Scholar 

  43. H. Gao, M. J. Zahr and J.-X. Wang, Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems, Computer Methods in Applied Mechanics and Engineering, 390 (2022) 114502.

    Article  MathSciNet  Google Scholar 

  44. W. Liu and M. J. Pyrcz, Physics-informed graph neural network for spatial-temporal production forecasting, Geoenergy Science and Engineering, 223 (2023) 211486.

    Article  Google Scholar 

  45. M. Yang and J. T. Foster, Multi-output physics-informed neural networks for forward and inverse PDE problems with uncertainties, Computer Methods in Applied Mechanics and Engineering, 402 (2022) 115041.

    Article  Google Scholar 

  46. P.-H. Chiu et al., CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method, Computer Methods in Applied Mechanics and Engineering, 395 (2022) 114909.

    Article  MathSciNet  Google Scholar 

  47. C. L. Wight and J. Zhao, Solving allen-cahn and cahn-hilliard equations using the adaptive physics informed neural networks, arXiv:2007.04542 (2020) DOI: https://doi.org/10.48550/arXiv.2007.05452.

  48. S. Wang, Y. Teng and P. Perdikaris, Understanding and mitigating gradient flow pathologies in physics-informed neural networks, SIAM Journal on Scientific Computing, 43 (5) (2021) 3055–3081.

    Article  MathSciNet  Google Scholar 

  49. J. Yu et al., Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems, Computer Methods in Applied Mechanics and Engineering, 393 (2022) 114823.

    Article  MathSciNet  Google Scholar 

  50. F. Xiong et al., Gradient-weighted physics-informed neural networks for one- dimensional euler equation dimensional euler equation, TechRxiv. (2022) DOI: https://doi.org/10.36227/techrxiv.20099957.v1(Preprint).

  51. Y. Liu et al., Physics-informed neural networks based on adaptive weighted loss functions for Hamilton-Jacobi equations, Mathematical Biosciences and Engineering, 19 (12) (2022) 12866–12896.

    Article  Google Scholar 

  52. S. Wang, X. Yu and P. Perdikaris, When and why PINNs fail to train: a neural tangent kernel perspective, Journal of Computational Physics, 449 (2022) 110768.

    Article  MathSciNet  Google Scholar 

  53. D. Liu and Y. Wang, A dual-dimer method for training physics-constrained neural networks with minimax architecture, Neural Networks, 136 (2021) 112–125.

    Article  Google Scholar 

  54. L. D. McClenny and U. M. Braga-Neto, Self-adaptive physics-informed neural networks, Journal of Computational Physics, 474 (2023) 111722.

    Article  MathSciNet  Google Scholar 

  55. P. Nasiri and R. Dargazany, Reduced-PINN: an integration-based physics-informed neural networks for stiff ODEs, arXiv:2208.12045v1 (2022) DOI: https://doi.org/10.48550/arXiv.2208.12045.

  56. S. Maddu et al., Inverse dirichlet weighting enables reliable training of physics informed neural networks, Machine Learning: Science and Technology, 3 (1) (2022) 015026.

    Google Scholar 

  57. E. Kharazmi, Z. Zhang and G. E. Karniadakis, Variational physics-informed neural networks for solving partial differential equations, arXiv:1912.00873 (2019) DOI: https://doi.org/10.48550/arXiv.1912.00873.

  58. R. Khodayi-Mehr and M. Zavlanos, VarNet: variational neural networks for the solution of partial differential equations, Proceedings of the 2nd Conference on Learning for Dynamics and Control (2020) 298–307.

  59. E. Kharazmi, Z. Zhang and G. E. M. Karniadakis, hp-VPINNs: variational physics-informed neural networks with domain decomposition, Computer Methods in Applied Mechanics and Engineering, 374 (2021) 113547.

    Article  MathSciNet  Google Scholar 

  60. W. E. and B. Yu, The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics, 6 (1) (2018) 1–12.

    Article  MathSciNet  Google Scholar 

  61. J. Bai et al., A physics-informed neural network technique based on a modified loss function for computational 2D and 3D solid mechanics, Computational Mechanics, 71 (2022) 1–20.

    MathSciNet  Google Scholar 

  62. C. Wang et al., Is L2 physics-informed loss always suitable for training physics-informed neural network? Advances in Neural Information Proceeding Systems 35 (NeurIPS 2022), New Orleans, USA (2022).

  63. C. Davi and U. Braga-Neto, PSO-PINN: physics-informed neural networks trained with particle swarm optimization, arXiv:2202.01943 (2022) DOI: https://doi.org/10.48550/arXiv.2202.01943.

  64. B. Lu, C. Moya and G. Lin, NSGA-PINN: a multi-objective optimization method for physics-informed neural network training, Algorithms, 16 (4) (2023) 194.

    Article  Google Scholar 

  65. M. A. Nabian, R. J. Gladstone and H. Meidani, Efficient training of physics-informed neural networks via importance sampling, Computer-Aided Civil and Infrastructure Engineering, 36 (8) (2021) 962–977.

    Article  Google Scholar 

  66. Z. Yang, Z. Qiu and D. Fu, DMIS: dynamic mesh-based importance sampling for training physics-informed neural networks, arXiv:2211.13944 (2022) DOI: https://doi.org/10.48550/arXiv.2211.13944.

  67. D. He et al., Learning physics-informed neural networks without stacked back-propagation, arXiv:2202.09340 (2022) DOI: https://doi.org/10.48550/arXiv.2202.09340.

  68. S. Markidis, The old and the new: can physics-informed deep-learning replace traditional linear solvers?, Frontiers in Big Data, 4 (2021).

  69. A. D. Jagtap, E. Kharazmi and G. E. Karniadakis, 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 (2020) 113028.

    Article  MathSciNet  Google Scholar 

  70. X. Meng et al., PPINN: parareal physics-informed neural network for time-dependent PDEs, Computer Methods in Applied Mechanics and Engineering, 370 (2020) 113250.

    Article  MathSciNet  Google Scholar 

  71. A. D. Jagtap and G. E. Karniadakis, 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) (2020) https://doi.org/10.4208/cicp.oa-2020-0164.

  72. P. Stiller et al., Large-scale neural solvers for partial differential equations, Driving Scientific and Engineering Discoveries Through the Convergence of HPC, Big Data and AI., Cham: Springer International Publishing (2020).

    Google Scholar 

  73. Z. Hu et al., Augmented Physics-Informed Neural Networks (APINNs): a gating network-based soft domain decomposition methodology, arXiv:2211.08939 (2022) DOI: https://doi.org/10.48550/arXiv.2211.08939.

  74. S. Wang, S. Sankaran and P. Perdilcaris, Respecting causality is all you need for training physics-informed neural networks, arXiv:2203.07404 (2022) DOI: https://doi.org/10.48550/arXiv.2203.07404.

  75. A. Daw et al., Mitigating propagation failures in PINNs using evolutionary sampling, arXiv:2207.02338 (2022) DOI: https://doi.org/10.48550/arXiv.2207.02338.

  76. A. E. Eiben and J. E. Smith, Introduction to Evolutionary Computing, Springer-Verlag Berlin Heidelberg, Germany (2015).

    Book  Google Scholar 

  77. J. Guo, H. Wang and C. Hou, A novel adaptive causal sampling method for physics-informed neural networks, arXiv:2210.12914 (2022) DOI: https://doi.org/10.48550/arXiv.2210.12914.

  78. R. Mattey and S. Ghosh, A novel sequential method to train physics informed neural networks for allen cahn and cahn hilliard equations, Computer Methods in Applied Mechanics and Engineering, 390 (2022) 114474.

    Article  MathSciNet  Google Scholar 

  79. M. Penwarden et al., A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions, arXiv:2302.14227 (2023) DOI: https://doi.org/10.48550/arXiv.2302.14227.

  80. A. F. Psaros, K. Kawaguchi and G. E. Karniadakis, Meta-learning PINN loss functions, Journal of Computational Physics, 458 (2022) 111121.

    Article  MathSciNet  Google Scholar 

  81. S. Goswami et al., Transfer learning enhanced physics informed neural network for phase-field modeling of fracture, Theoretical and Applied Fracture Mechanics, 106 (2020) 102447.

    Article  Google Scholar 

  82. B. Bahmani and W. Sun, Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learnings, arXiv:2107.11496 (2021) DOI: https://doi.org/10.48550/arXiv.2107.11496.

  83. S. Desai et al., One-shot transfer learning of physics-informed neural networks, arXiv:2110.11286 (2021) DOI: https://doi.org/10.48550/arXiv.2110.11286.

  84. C. Xu et al., Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios, Computer Methods in Applied Mechanics and Engineering, 405 (2023) 115852.

    Article  MathSciNet  Google Scholar 

  85. M. Penwarden et al., A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs, Journal of Computational Physics, 477 (2023) 111912.

    Article  MathSciNet  Google Scholar 

  86. W. Chen et al., Physics-informed machine learning for reduced-order modeling of nonlinear problems, Journal of Computational Physics, 446 (2021) 110666.

    Article  MathSciNet  Google Scholar 

  87. K. Haitsiukevich and A. Ilin, Improved training of physics-informed neural networks with model ensembles, arXiv:2204.05108 (2022) DOI: https://doi.org/10.48550/arXiv.2204.05108.

  88. J. Kim et al., DPM: a novel training method for physics-informed neural networks in extrapolation, Proceedings of the AAAI Conference on Artificial Intelligence, 35 (9) (2021) 8146–8154.

    Article  Google Scholar 

  89. K. Linka et al., Bayesian physics informed neural networks for real-world nonlinear dynamical systems, Computer Methods in Applied Mechanics and Engineering, 402 (2022) 115346.

    Article  MathSciNet  Google Scholar 

  90. J. Sirignano and K. Spiliopoulos, DGM: a deep learning algorithm for solving partial differential equations, Journal of Computational Physics, 375 (2018) 1339–1364.

    Article  MathSciNet  Google Scholar 

  91. B. Chudomelka et al., Deep neural network for solving differential equations motivated by legendre-galerkin approximation, arXiv:2010.12975 (2020) DOI: https://doi.org/10.48550/arXiv.2010.12975.

  92. J. Choi, N. Kim and Y. Hong, Unsupervised legendre-galerkin neural network for solving partial differential equations, IEEE Access, 11 (2023) 23433–23446.

    Article  Google Scholar 

  93. S. Amini Niaki et al., Physics-informed neural network for modelling the thermochemical curing process of composite-tool systems during manufacture, Computer Methods in Applied Mechanics and Engineering, 384 (2021) 113959.

    Article  MathSciNet  Google Scholar 

  94. H. K. Lee and S. In, Neural algorithm for solving differential equations, Journal of Computational Physics, 91 (1990) 110–131.

    Article  MathSciNet  Google Scholar 

  95. D. C. U. Psichogios and H. Lyle, A hybrid neural network-first principles approach to process modeling, AIChE J., 38 (1992) 1499–1511.

    Article  Google Scholar 

  96. M. W. M. G. Dissanayake and N. Phan-Thien, Neural-network-based approximations for solving partial differential equations, Communications in Numerical Methods in Engineering, 10 (1994) 195–201.

    Article  Google Scholar 

  97. I. E. Lagaris, A. Likas and D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Neural Networks, 9 (1998) 987–1000.

    Article  Google Scholar 

  98. P. Ramuhalli, L. Udpa and S. S. Udpa, Finite-element neural networks for solving differential equations, IEEE Transactions on Neural Networks, 16 (6) (2005) 1381–1392.

    Article  Google Scholar 

  99. A. S. B. Malek, Numerical solution for high order differential equations using a hybrid neural network—optimization method, Applied Mathematics and Computation, 183 (2006) 260–271.

    Article  MathSciNet  Google Scholar 

  100. R. M. Shekari Beidokhti, Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques, Journal of the Franklin Institute, 346 (2009) 898–913.

    Article  MathSciNet  Google Scholar 

  101. M. Kumar and N. Yadav, Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey, Computers & Mathematics with Applications, 62 (2011) 3796–3811.

    Article  MathSciNet  Google Scholar 

  102. A. Griewank, On Automatic differentiation and algorithmic linearization, Pesquisa Operacional, 34 (3) (2014) 621–645.

    Article  Google Scholar 

  103. M. B. Abadi et al., TensorFlow: a system for large-scale machine learning, Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI 16), Savannah, GA, USA (2016).

  104. M. P. Raissi, Paris karniadakis, george em, physics informed deep learning (part I): data-driven solutions of nonlinear partial differential equations, arXiv:1711.10561 (2017) DOI: https://doi.org/10.48550/arXiv.1711.10561.

  105. M. Raissi, P. Perdikaris and G. E. Karniadakis, Physics informed deep learning (part II): data-driven discovery of nonlinear partial differential equations, arXiv:1711.10566 (2017) DOI: 10.48550.arXiv.1711.10566.

Download references

Acknowledgments

This research was supported by Korea Institute of Marine Science & Technology Promotion (KIMST) funded by the Ministry of Oceans and Fisheries (20220210).

Author information

Authors and Affiliations

  1. PIDOTECH Inc., 114, Beobwon-ro, Songpa-gu, Seoul, 05854, Korea

    Ikhyun Ryu, Gyu-Byung Park, Yongbin Lee & Dong-Hoon Choi

Authors
  1. Ikhyun Ryu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gyu-Byung Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yongbin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dong-Hoon Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong-Hoon Choi.

Additional information

Ikhyun Ryu received a B.S. degree in Mechanical Engineering from Karlsruhe Institute of Technology, Karlsruhe, Germany, in 2019. He then received a M.S. degree in Mechanical Engineering from Hanyang University, Seoul, South Korea, in 2022. He is now a Senior Research Engineer in PIDOTECH Inc. since 2022. His research interests include heat transfer, multidisciplinary design optimization, and Physics-Informed Neural Networks.

Gyu-Byung Park received a B.S. degree in Mechanical Engineering from Hanyang University, South Korea, in 2006. He then received a Ph.D. degree in Mechanical Engineering from Hanyang University, South Korea, in 2016. He is now a Senior Research Engineer in PIDOTECH Inc. since 2016. His research interests include Artificial Intelligence, Deep Learning, Design Optimization and Physics-Informed Neural Networks.

Yongbin Lee received a B.S. degree in Mechanical Engineering from Hanyang University, Seoul, South Korea, in 2002. He then received a M.S. degree in Mechanical Engineering from Hanyang University, Seoul, South Korea, in 2004. He then received a Ph.D. degree in Mechanical Engineering from Hanyang University, Seoul, South Korea, in 2009. He is now a Senior Research Engineer in PIDOTECH since 2012. His research interests include Machine Learning, Metamodeling, Design of Experiments, and Design Optimization.

Dong-Hoon Choi graduated from Seoul National University with a B.S. in mechanical engineering in 1975. He then graduated from KAIST in 1977 with an M.S. in Mechanical Engineering. He earned his Ph.D. in mechanical engineering from the University of Wisconsin-Madison. From 1986 to 2018, he served as a Professor of Mechanical Engineering at Hanyang University. He has been the CEO of PIDOTECH Inc. since 2003. His research interest includes AI-aided design optimization, multidisciplinary design optimization, surrogate-based design optimization, and AI applications for simulation and engineering design.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ryu, I., Park, GB., Lee, Y. et al. Physics-informed neural network for engineers: a review from an implementation aspect. J Mech Sci Technol 38, 3499–3519 (2024). https://doi.org/10.1007/s12206-024-0624-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-024-0624-9

Keywords

Search

Navigation