Application of differential equations in neural networks
محورهای موضوعی : journal of Artificial Intelligence in Electrical Engineering
1 - دانشگاه آزاد اسلامی واحد اهر
کلید واژه: artificial intelligence, Neural Differential Equations, differential equation, ,
چکیده مقاله :
Differential equations play a key role in the environmental sciences and provide mathematical tools for understanding environmental processes and predicting changes.
The purpose of the research is to provide mathematical modeling methods to solve environmental problems and to use standard mathematical techniques and methods to solve the model by obtaining the desired results, and the analysis is done based on mathematical laws and ecological system.
In this research, the application of differential equations for environmental modeling, especially in pollutant dispersion, ecosystem dynamics, and climate change prediction, is discussed. In this research, mathematical foundations, modeling method through differential equation is examined and its role in explaining the complexity of the environmental system is revealed.
This paper also points to the potential for future development of differential equations in interdisciplinary topics and more advanced computing, which provides a research context and improvement path for the field of environmental sciences.
[1] ShinY.-H. et al. “ Hopfield-type neural ordinary differential equation for robust machine learning ”, Pattern Recognit Lett, 2021.
[2] LeiD. et al.” Neural ordinary differential grey model and its applications “ Expert Syst Appl, 2021.
[3] K. Diethelm, “The Analysis of Fractional Differential Equations “, Springer-Verlag, Berlin, 2010.
[4] C. Li and F. Zeng, “ Numerical Methods for Fractional Calculus “, CRC press, New York, 2015.
[5] I. Podlubny, “ Fractional Differential Equations. Academic Press “, San Diego and London, 1999.
[6] Atangana, A.,Baleanu, D., and Alsaed . A.(2016),“Analysis of time-fractional Hunter–Saxton equation: a model of neumatic liquid crystal”inOpen
Phys.,14:145-149,2016.
[7] Khalil, R.,Al Horani, M.,Yousef, A., and Sababheh, M.(2014),“A new definition of fractional derivative, 264 (2014) 65–70.”inJ. Comput. Appl. Math.,264:65-70,2014.
[8] Yusuf, A.,Inc,M., Aliyu, A.I., and Baleanu, D. (2019),“Optical Solitons Possessing Beta Derivative of the ChenLee-Liu Equation in Optical Fibers,”in Front. Phys.,
7:1-7,2019.
[9] Chen, Ricky T. Q.; Rubanova, Yulia; Bettencourt, Jesse; Duvenaud, David K. "Neural Ordinary Differential Equations" In Bengio, (2018).
[10] S.; Wallach, H.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; Garnett, R. (eds.). “ Advances in Neural Information Processing Systems”. Vol. 31. Curran Associates, Inc. arXiv:1806.07366.
