Abstract: Physics-Informed neural networks (PINNs) are one of the most active frontiers in scientific machine learning, used to solve the forward and inverse problems governed by partial differential equations. It incorporates governing physical laws and equations into neural network training i.e., loss function. This review discusses twenty-four primary sources, beginning with the biological inspiration and architecture of artificial neural networks, proceeds....
Key Word: Physics-informed neural networks; PINNs; adaptive sampling; collocation points; spectral bias; neural tangent kernel; scientific machine learning; heat transfer.
[1] Maind, S. B., & Wankar, P. (2014). Research paper on basic of artificial neural network. International Journal on Recent and Innovation Trends in Computing and Communication, 2(1), 96-100.
[2] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). 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.DOI: 10.1016/j.jcp.2018.10.045. https://doi.org/10.1016/j.jcp.2018.10.045.
[3] Cuomo, S., Di Cola, V. S., Giampaolo, F., Rozza, G., Raissi, M., & Piccialli, F. (2022). Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Journal of scientific computing, 92(3), 88.DOI: 10.1007/s10915-022-01939-z. arXiv:2201.05624. https://doi.org/10.1007/s10915-022-01939-z.
[4] Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). DeepXDE: A deep learning library for solving differential equations. SIAM review, 63(1), 208-228. DOI: 10.1137/19M1274067. arXiv:1907.04502. https://doi.org/10.1137/19M1274067.
