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Optimization functions for neural network-based approximation of Burger’s–Fisher equation: A comparative analysis | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 01 تیر 1404 اصل مقاله (356.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34512.5156 | ||
| نویسندگان | ||
| Hanieh Hajinezhad1؛ Abulfazl Yavari* 2؛ Seyyed Mohammad Reza Hashemi3 | ||
| 1Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| 2Department of Computer Engineering and IT, Payame Noor University, Tehran, Iran | ||
| 3Faculty of Mathematics, Statistics Computer Science, Semnan University, Semnan, Iran | ||
| تاریخ دریافت: 02 تیر 1403، تاریخ پذیرش: 05 شهریور 1403 | ||
| چکیده | ||
| This study explores the effectiveness of different optimization functions for approximating the solution of Burger’s–Fisher equation with initial and boundary conditions based on neural networks. It compares and analyzes the performance of nine common optimization functions, emphasizing computational accuracy. Extensive experiments show that the choice of appropriate optimization function significantly influences the performance of neural network-based solvers for approximating the solution of Burger’s–Fisher equation with initial and boundary conditions. The findings provide valuable insights and practical recommendations for researchers applying neural networks to solve Berger's equation in fields such as fluid dynamics and heat transfer. | ||
| کلیدواژهها | ||
| Burger’s–Fisher equation؛ Neural networks؛ Optimization functions | ||
| مراجع | ||
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[1] L.P. Aarts and P. Van der Veer, Solving nonlinear differential equations by a neural network method, Int. Conf. Comput. Sci., Springer, 2001. [2] F. Chen, D. Sondak, P. Protopapas, M. Mattheakis, S. Liu, D. Agarwal, and M. Di Giovanni, Neurodiffeq: A python package for solving differential equations with neural networks, J. Open Source Software 5 (2020), no. 46, 1931. [3] 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), no. 4, 423. [4] T. Dozat, Incorporating nesterov momentum into adam, Workshop track-ICLR, 2016. [5] A. Fallah and M.M. Aghdam, Physics-informed neural network for solution of nonlinear differential equations, Nonlinear Approaches in Engineering Application: Automotive Engineering Problems, Cham: Springer Nature Switzerland, 2024, pp. 163–178. [6] B. Gurbuz and M. Sezer, A modified laguerre matrix approach for burgers–fisher type nonlinear equations,Numerical Solutions of Realistic Nonlinear Phenomena, Springer, 2020, pp. 107-123. [7] H. Hajinezhad, A numerical approximation for the one-dimensional burger–fisher equation, Asian Res. J. Math. 18 (2022), no. 5, 22–30. [8] D.P. Kingma, Adam: a method for stochastic optimization, arXiv preprint arXiv:1412.6980 (2014). [9] I.E. Lagaris, A. Likas, and D.I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Networks 9 (1998), no. 5, 987–1000. [10] L. Liu, H. Jiang, P. He, W. Chen, X. Liu, J. Gao, and J. Han, On the variance of the adaptive learning rate and beyond, arXiv preprint arXiv:1908.03265 (2019). [11] I. Loshchilov and F. Hutter, Decoupled weight decay regularization, arXiv preprint arXiv:1711.05101 (2017). [12] L. Lu, X. Meng, Z. Mao, and G.E. Karniadakis Deepxde: A deep learning library for solving differential equations, SIAM Rev. 63 (2021), no. 1, 208–228. [13] R.K. Mohanty and S. Sharma, A high-resolution method based on off-step non-polynomial spline approximations for the solution of Burgers-Fisher and coupled nonlinear Burgers’ equations, Engin. Comput. 37 (2020), no. 8, 2785–2818. [14] K. Parand, A.A. Aghaei, S. Kiani, T.I. Zadeh, and Z. Khosravi, A neural network approach for solving nonlinear differential equations of Lane–Emden type, Engin. Comput. 40 (2024), no. 2, 953–969. [15] M.A. Pirdawood and Y.A. Sabawi, High-order solution of generalized Burgers–Fisher equation using compact finite difference and dirk methods, J. Phys.: Conf. Ser. 1999 (2021), no. 1, 012088. [16] M. Riedmiller and H. Braun, A direct adaptive method for faster backpropagation learning: The RPROP algorithm, Proc. IEEE Int. Conf. Neural Networks, 1993, pp. 586—591. [17] H. Robbins and S. Monro, A stochastic approximation method, Ann. Math. Statist. 25 (1951), 400–407. [18] A. Singh, S. Dahiya, and S. Singh, A fourth-order b-spline collocation method for nonlinear Burgers–Fisher equation, Math. Sci. 14 (2020), no. 1, 75–85. [19] P. Venkatachalapathy and S. Mallikarjunaiah, A deep learning neural network framework for solving singular nonlinear ordinary differential equations, Int. J. Appl. Comput. Math. 9 (2023), no. 5, 68. [20] Y. Wen and T. Chaolu, Study of Burgers–Huxley equation using neural network method, Axioms 12 (2023), no. 5, 429. [21] Y. Ye, X. Liu, Y. Li, H. Fan, and H. Zhang, Deep neural network method for solving the fractional Burgers-type equations with conformable derivative, Phys. Scripta 98 (2023), no. 6, 065214. [22] C.G. Zhu and W.S. Kang, Numerical solution of Burgers–Fisher equation by cubic b-spline quasi-interpolation, Appl. Math. Comput. 216 (2010), 2679–2686. | ||
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