Author:
Uddin Ziya,Ganga Sai,Asthana Rishi,Ibrahim Wubshet
Abstract
AbstractIn this study, the applicability of physics informed neural networks using wavelets as an activation function is discussed to solve non-linear differential equations. One of the prominent equations arising in fluid dynamics namely Blasius viscous flow problem is solved. A linear coupled differential equation, a non-linear coupled differential equation, and partial differential equations are also solved in order to demonstrate the method’s versatility. As the neural network’s optimum design is important and is problem-specific, the influence of some of the key factors on the model’s accuracy is also investigated. To confirm the approach’s efficacy, the outcomes of the suggested method were compared with those of the existing approaches. The suggested method was observed to be both efficient and accurate.
Publisher
Springer Science and Business Media LLC
Reference67 articles.
1. Dissanayake, M. W. M. G. & Phan-Thien, N. Neural-network-based approximations for solving partial differential equations. Commun. Numer. Methods Eng. 10, 195–201 (1994).
2. Lagaris, I. E., Likas, A. & Fotiadis, D. I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw. 9, 987–1000 (1998).
3. Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv:1711.10561 [cs.AI] (2017).
4. Tartakovsky, A. M., Marrero, C. O., Perdikaris, P., Tartakovsky, G. D. & Barajas-Solano, D. Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems. Water Resour. Res. 56, e2019WR026731 (2020).
5. Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019).
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献