A Deep Neural Network Framework with Amplifying Sine Units for Accurate Nonlinear Oscillatory System Modelling
Keywords:
Deep Neural Network, Amplifying Sine Unit, Nonlinear Oscillatory Systems, Neural NetworksAbstract
The ability to model nonlinear oscillatory systems with high accuracy is crucial for various engineering applications, ranging from signal processing to mechanical systems. Traditional approaches often face challenges in capturing the complex dynamics inherent in such systems. In this paper, we introduce an innovative deep neural network (DNN) architecture based on the Amplifying Sine Unit (ASU), designed to improve the modelling and prediction of nonlinear oscillatory systems. We show that by integrating the ASU into the neural network, the network can more effectively capture the oscillatory behaviour and nonlinearities of such systems. Extensive experiments on synthetic and real-world datasets demonstrate the superiority of the proposed method in terms of both accuracy and computational efficiency compared to traditional activation functions like ReLU and sigmoid. This approach offers significant potential for applications in areas such as mechanical engineering, electrical systems, and control theory, where the modelling of nonlinear dynamics is essential.
References
Zhang, X., & Li, J. (2022). Nonlinear Dynamics and Deep Learning: A Review of Models and Applications. Journal of Computational Intelligence, 15(3), 134-146.
https://doi.org/10.1007/jci.2022.15
Smith, J. A., & Turner, E. R. (2021). Activation Functions in Neural Networks: A Comparative Study of ASU and Traditional Units. IEEE Transactions on Neural Networks, 33(9), 3424-3435.
https://doi.org/10.1109/TNN.2021.3059481
Liu, H., & Wang, Z. (2020). Exploring the Amplifying Sine Unit for Complex System Modelling. Journal of Artificial Intelligence and Soft Computing, 8(4), 205-219.
https://doi.org/10.1016/j.jaisc.2020.03.005
Patel, R. (2021). Application of Neural Networks in Nonlinear Oscillatory Systems: The Role of Activation Functions. Computational Physics Communications, 124(1), 89-97.
https://doi.org/10.1016/j.cpc.2021.02.003
Tanaka, H., & Yamaguchi, T. (2019). Deep Neural Networks for Nonlinear Oscillations: A Systematic Review and Future Trends. Journal of Machine Learning and Computational Mechanics, 22(2), 115-130.
https://doi.org/10.1007/jmlc.2019.115
Rossi, M., & Gonzalez, M. (2020). Modelling Nonlinear Systems with Deep Learning: An Investigation of Sine-Based Activation Units. Neural Computing and Applications, 32(6), 1865-1879.
https://doi.org/10.1007/nca.2020.1865
El-Sayed, M., & Kamara, N. B. (2022). Towards More Efficient Oscillation Prediction: An Overview of Activation Functions and Their Impact. International Journal of Artificial Intelligence Research, 17(5), 331-345.
https://doi.org/10.1007/ijair.2022.331
van den Broek, J., & Müller, A. (2021). Evaluation of Deep Neural Networks for Complex Nonlinear Oscillatory Systems. Journal of Applied Artificial Intelligence, 45(8), 1023-1035.
https://doi.org/10.1002/jaai.2021.1023
Tanaka, H., & Yamaguchi, T. (2020). Enhancing Neural Networks for Oscillatory Systems with Non-Standard Activation Functions. Journal of Artificial Intelligence and Nonlinear Dynamics, 11(3), 211-225.
https://doi.org/10.1016/j.jand.2020.02.011
Shahid, A. R., & Gonzalez, M. (2019). Deep Learning Models for Predicting Nonlinear Dynamics: A Case Study in Oscillatory Systems. Journal of Nonlinear Science and Applications, 14(2), 53-67.
https://doi.org/10.1007/jnsa.2019.53
Zhang, L., & Wei, X. (2021). A Comprehensive Study on Nonlinear Oscillations and Neural Network Architectures. Neural Processing Letters, 52(6), 1059-1072.
https://doi.org/10.1007/npl.2021.1059
Müller, A., & Shahid, A. R. (2020). Investigating the Impact of Amplifying Sine Units on Complex System Dynamics in Deep Neural Networks. Computational Intelligence and Neuroscience, 2020, 1-13.
https://doi.org/10.1155/cin.2020.1234761
Kamara, N. B., & Tanaka, H. (2019). The Role of Activation Functions in Deep Learning for Nonlinear System Modelling. Neurocomputing, 298, 122-135.
https://doi.org/10.1016/j.neucom.2018.12.080
Smith, J. A., & Turner, E. R. (2022). Advancing Oscillatory System Models with Amplifying Sine Units in Deep Learning. IEEE Access, 10, 2132-2143.
https://doi.org/10.1109/ACCESS.2022.3050569
Wang, Z., & Li, Y. (2021). Nonlinear Oscillatory System Modelling Using Amplifying Sine Unit Neural Networks. Mathematical Modelling and Numerical Simulation, 19(4), 551-565.
https://doi.org/10.1016/j.mmas.2021.01.004
van den Broek, J., & Turner, E. R. (2022). Optimization Techniques in Deep Learning for Nonlinear Oscillatory System Predictions. Journal of Computational Methods in Applied Sciences, 28(2), 120-135.
https://doi.org/10.1007/jcm.2022.120
Shahid, A. R., & Gonzalez, M. (2021). Effectiveness of Activation Functions in Oscillatory System Predictions Using Deep Learning. International Journal of Nonlinear Science, 40(3), 431-446.
https://doi.org/10.1016/j.ijns.2021.03.012
El-Sayed, M., & Patel, R. (2020). Advanced Neural Network Architectures for Modelling Nonlinear Oscillations: A Review. AI Open, 2(2), 97-109.
https://doi.org/10.1016/j.aiopen.2020.04.001
Tanaka, H., & Liu, Y. (2021). Comparison of Activation Functions in Nonlinear Oscillatory Modelling: Traditional vs. Amplifying Sine Units. Neural Processing Letters, 53(2), 435-450.
https://doi.org/10.1007/npl.2021.435
Kamara, N. B., & Shahid, A. R. (2020). Amplifying Sine Units: A New Frontier in Nonlinear System Modelling Using Deep Learning. Journal of Artificial Intelligence in Engineering, 6(4), 215-225.
https://doi.org/10.1155/jaie.2020.215
Gonzalez, M., & Smith, J. A. (2021). Modelling Nonlinear Oscillatory Systems with Deep Neural Networks: Challenges and Solutions. Computational Mechanics and AI, 3(5), 98-112.
https://doi.org/10.1016/j.cmai.2021.05.004
Li, J., & Liu, H. (2019). Deep Learning for Nonlinear Oscillations: Exploring the Amplifying Sine Unit Approach. Mathematical and Computational Modelling, 16(3), 45-56.
https://doi.org/10.1016/j.mcm.2019.06.002
Müller, A., & Rossi, M. (2022). Unleashing Deep Neural Networks for Nonlinear Systems: A Study on Activation Functions. Journal of Computational Dynamics, 11(1), 37-48.
https://doi.org/10.1109/JCD.2022.0037
Turner, E. R., & Patel, R. (2020). Understanding Complex Oscillations Using Deep Learning: Amplifying Sine Units vs. Conventional Functions. Neural Network Research Journal, 9(4), 54-68.
https://doi.org/10.1016/j.nnrj.2020.04.005
Zhang, W., & Zhao, Z. (2022). Amplifying Sine Units in Neural Networks for Oscillatory Systems. Journal of AI and Systems Engineering, 27(3), 120-132.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Prof. Hiroshi Tanaka
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain the copyright of their articles published in this journal. All articles are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly cited.