Reduced order framework for 2D heat transfer simulation under variations of boundary conditions based on deep learning algorithms

نوع مقاله : مقاله پژوهشی کوتاه

نویسندگان

1 گروه مهندسی کامپیوتر، دانشگاه قم، قم، ایران.

2 آزمایشگاه تحقیقات توربولانس و احتراق، گروه مهندسی مکانیک، دانشگاه قم، قم، ایران.

چکیده

Due to the high computational cost of the direct numerical simulation methods of the governing equations of some natural phenomena, surrogate models based on machine learning methods such as deep learning algorithms have been commonly interested in modeling these phenomena. This paper proposes a reduced-order model based on a deep-learning algorithm to simulate temperature changes in a two-dimensional field. This model is developed using three different methods, including a framework based on convolutional neural networks, a physics-informed loss function of the phenomenon, and a reduced-order model using the autoencoder method. The model outcomes were compared with the results obtained from a high-resolution finite difference method. The results show that the reduced-order model (with an accuracy of 2.528×10-6 °C) has higher accuracy than the other two models. Meanwhile, the Model-based physics-informed loss is superior to the other two models in terms of steady-state temperature data consumption (only 400 data of size 8×8).

کلیدواژه‌ها


عنوان مقاله [English]

Reduced order framework for 2D heat transfer simulation under variations of boundary conditions based on deep learning algorithms

نویسندگان [English]

  • Somayeh Afzali 1
  • Mohammad Kazem Moayyedi 2
  • Faranak Fotouhi 1
1 Department of Computer Engineering, University of Qom, Qom, Iran.
2 Turbulence and Combustion Research Lab., Department of Mechanical Engineering, University of Qom, Qom, Iran.
چکیده [English]

Due to the high computational cost of the direct numerical simulation methods of the governing equations of some natural phenomena, surrogate models based on machine learning methods such as deep learning algorithms have been commonly interested in modeling these phenomena. This paper proposes a reduced-order model based on a deep-learning algorithm to simulate temperature changes in a two-dimensional field. This model is developed using three different methods, including a framework based on convolutional neural networks, a physics-informed loss function of the phenomenon, and a reduced-order model using the autoencoder method. The model outcomes were compared with the results obtained from a high-resolution finite difference method. The results show that the reduced-order model (with an accuracy of 2.528×10-6 °C) has higher accuracy than the other two models. Meanwhile, the Model-based physics-informed loss is superior to the other two models in terms of steady-state temperature data consumption (only 400 data of size 8×8).

کلیدواژه‌ها [English]

  • Steady-state heat transfer
  • Convolutional neural networks
  • Autoencoder
  • Reduced order model
  • Mean squared error
[1] J. Tompson, K. Schlachter, P. Sprechmann, and K. Perlin, “Accelerating eulerian fluid simulation with convolutional networks,” in 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Workshop Track Proceedings. OpenReview.net, 2017.
[2] M. Raissi, A. Yazdani, and G. E. Karniadakis, “Hidden fluid mechanics: A navierstokes informed deep learning framework for assimilating flow visualization data,” CoRR, vol. abs/1808.04327, 2018, doi: 10.48550/arXiv.1808.04327.
[3] M. Edalatifar, M. B. Tavakoli, M. Ghalambaz, and F. Setoudeh, “Using deep learning to learn physics of conduction heat transfer,” J. Therm. Anal. Calorim., vol. 146, pp. 1435–1452, 2021, doi: 10.1007/s10973-020-09875-6.
[4] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems 2012. Proceedings of a meeting held December 3-6, 2012, Lake Tahoe, Nevada, United States, P. L. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger, Eds., 2012, pp. 1106–1114.
[5] M. Johnson, M. Schuster, Q. V. Le, M. Krikun, Y.Wu, Z. Chen, N. Thorat, F. B. Viegas, M.Wattenberg, G. Corrado, M. Hughes, and J. Dean, “Google’s multilingual neural machine translation system: Enabling zero-shot translation,” Trans. Assoc. Comput. Linguistics, vol. 5, pp. 339–351, 2017, doi: 10.1162/TACL_A_00065.
[6] I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning. MIT Press, 2016.
[7] H. El-Amir and M. Hamdy, Deep Learning Pipeline: Building a Deep Learning Model with TensorFlow. Apress Berkeley, CA, 2020, doi: 10.1007/978-1-4842-5349-6.
[8] S. Afzali, M. K. Moayyedi, and F. Fotouhi, “Development of an equation-free reduced-order model based on different feature extraction patterns on the two-dimensional steady-state heat transfer dataset,” Soft Comput. J., vol. 10, no. 1, pp. 16–31, 2021, doi: 10.22052/scj.2021.242830.0 [In Persian].
[9] O. Ronneberger, P. Fischer, and T. Brox, “Unet: Convolutional networks for biomedical image segmentation,” in Medical Image Computing and Computer-Assisted Intervention - MICCAI 2015 - 18th International Conference Munich, Germany, October 5 - 9, 2015, Proceedings, Part III, ser. Lecture Notes in Computer Science, N. Navab, J. Hornegger, W. M. W. III, and A. F. Frangi, Eds., vol. 9351. Springer, 2015, pp. 234–241, doi: 10.1007/978-3-319-24574-4_28.
[10] R. Sharma, A. B. Farimani, J. Gomes, P. K. Eastman, and V. S. Pande, “Weakly-supervised deep learning of heat transport via physics informed loss,” CoRR, vol. abs/1807.11374, 2018, doi: 10.48550/arXiv.1807.11374.