THE DEEP NEURAL NETWORK-A REVIEW
Deep neural networks are considered the backbone of artificial intelligence, we will present a review of an article about the importance of neural networks and their role in other sciences, their characteristic, networks architecture, types, mathematical definition of deep neural networks, as well as their applications.
.Anderson, J. A. (2003). An Introduction to neural networks. Prentice Hall.
 Andrade-Loarca.H, Kutyniok.G,Oktem .O, and Petersen.P, (2019), Extraction of digital wavefront sets using ¨ applied harmonic analysis and deep neural networks. SIAM J. Imaging Sci. 12, 1936–1966.
 Andrade-Loarca.H, Kutyniok.G, Oktem.O, and Petersen.P , (2021), Deep Microlocal Reconstruction for Limited- ¨ Angle Tomography, arXiv:2108.05732.
 Bach.S, Binder.A, Montavon.G, Klauschen.F, M¨uller.K.R, and Samek.W, (2015), On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PLoS ONE 10 ,e0130140.
 Belkin.M, Hsu.D, Ma.S, and Mandal.S, (2019), Reconciling modern machine-learning practice and the classical bias–variance trade-off. Proc. Natl. Acad. Sci. USA 116 ,15849–15854.
 Berner.J, Grohs.P, Kutyniok.G, and Petersen.P,(2021), The Modern Mathematics of Deep Learning. In: Mathematical Aspects of Deep Learning, Cambridge University Press, to appear.
 ¨olcskei H.B, Grohs.P, Kutyniok .G, and Petersen.P, (2019), Optimal Approximation with Sparsely Connected Deep Neural Networks. SIAM J. Math. Data Sci. 1 ,8–45.
Cheng, B. and Titterington, D. M. (1994). Neural networks: A review from a statistical perspective. Statistical Science, 9, 2-54
 Cybenko.G (1989), Approximation by superpositions of a sigmoidal function. Math. Control Signal 2 (, 303– 314.
Dewolf, E.D., and Francl, L.J., (1997). Neural networks that distinguish in period of wheat tan spot in an outdoor environment Phytopathalogy, 87, 83-87.
Dewolf, E.D. and Francl, L.J. (2000) Neural network classification of tan spot and stagonespore blotch infection period in wheat field environment. Phytopathalogy, 20-,108-113.
 D Donoho.D, (2001), Sparse components of images and optimal atomic decompositions. Constr. Approx. 17 ,353–382.
 E.W and B. Yu. (2018), The deep ritz method: a deep learning-based numerical algorithm for solving variational problems. Commun. Math. Stat. 6 ,1–12.
Gaudart, J. Giusiano, B. and Huiart, L. (2004). Comparison of the performance of multi-layer perceptron and linear regression for epidemiological data. Comput. Statist. & Data Anal., 44, 547-70.
Hassoun, M. H. (1995). Fundamentals of Artificial Neural Networks. Cambridge: MIT Press.
Hopfield, J.J. (1982). Neural network and physical system with emergent collective computational capabilities. In proceeding of the National Academy of Science(USA79), 2554-2558
Kaastra, I. and Boyd, M.(1996). Designing a neural network for forecasting financial and economic time series. Neurocomputing, 10, 215-236.
Kohzadi, N., Boyd, S.M., Kermanshahi, B. and Kaastra, I. (1996). A comparision of artificial neural network and time series models for forecasting commodity prices Neurocomputing, 10, 169-181.
Kumar, M., Raghuwanshi, N. S., Singh, R,. Wallender, W. W. and Pruitt, W. O. (2002)Estimating Evapotranspiration using Artificial Neural Network. Journal of Irrigation and Drainage Engineering, 128, 224-233
Masters, T. (1993). Practical neural network recipes in C++, Academic press, NewYork.
Mcculloch, W.S. and Pitts, W. (1943) A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophy., 5, 115-133
Pal, S. Das, J. Sengupta, P. and Banerjee, S. K. (2002). Short term prediction of atmospheric temperature using neural networks. Mausam, 53, 471-80
Patterson, D. (1996). Artificial Neural Networks. Singapore: Prentice Hall.
Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage ang organization in the brain. Psychological review, 65, 386-408.
Rumelhart, D.E., Hinton, G.E and Williams, R.J. (1986). “Learning internal representation by error propagation”, in Parallel distributed processing: Exploration in microstructure of cognition, Vol. (1) ( D.E. Rumelhart, J.L. McClelland and the PDP research gropus, edn.) Cambridge, MA: MIT Press, 318-362.
Saanzogni, Louis and Kerr, Don (2001) Milk production estimate using feed forward artificial neural networks. Computer and Electronics in Agriculture, 32, 21-30.
Warner, B. and Misra, M. (1996). Understanding neural networks as statistical tools American Statistician, 50, 284-93.
Yegnanarayana, B. (1999). Artificial Neural Networks. Prentice Hall .
Zhang, G., Patuwo, B. E. and Hu, M. Y. (1998). Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting, 14, 35-62.
Copyright (c) 2023 IJRDO -JOURNAL OF MATHEMATICS
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere. Author(s) agree to the terms that the IJRDO Journal will have the full right to remove the published article on any misconduct found in the published article.