Frontiers in Emerging Engineering & Technologies

Open Access Peer Review International
Open Access

A Deep Neural Network Framework with Amplifying Sine Units for Accurate Nonlinear Oscillatory System Modelling

4 Graduate School of Engineering, University of Tokyo, Japan

Abstract

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.

How to Cite

Prof. Hiroshi Tanaka. (2025). A Deep Neural Network Framework with Amplifying Sine Units for Accurate Nonlinear Oscillatory System Modelling. Frontiers in Emerging Engineering & Technologies, 2(01), 6–12. Retrieved from https://irjernet.com/index.php/feet/article/view/111

References

πŸ“„ Zhang, X., & Li, J. (2022). Nonlinear Dynamics and Deep Learning: A Review of Models and Applications. Journal of Computational Intelligence, 15(3), 134-146.
πŸ“„ 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.
πŸ“„ 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.
πŸ“„ Patel, R. (2021). Application of Neural Networks in Nonlinear Oscillatory Systems: The Role of Activation Functions. Computational Physics Communications, 124(1), 89-97.
πŸ“„ 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.
πŸ“„ 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.
πŸ“„ 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.
πŸ“„ van den Broek, J., & MΓΌller, A. (2021). Evaluation of Deep Neural Networks for Complex Nonlinear Oscillatory Systems. Journal of Applied Artificial Intelligence, 45(8), 1023-1035.
πŸ“„ 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.
πŸ“„ 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.
πŸ“„ Zhang, L., & Wei, X. (2021). A Comprehensive Study on Nonlinear Oscillations and Neural Network Architectures. Neural Processing Letters, 52(6), 1059-1072.
πŸ“„ MΓΌller, 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.
πŸ“„ Kamara, N. B., & Tanaka, H. (2019). The Role of Activation Functions in Deep Learning for Nonlinear System Modelling. Neurocomputing, 298, 122-135.
πŸ“„ Smith, J. A., & Turner, E. R. (2022). Advancing Oscillatory System Models with Amplifying Sine Units in Deep Learning. IEEE Access, 10, 2132-2143.
πŸ“„ Wang, Z., & Li, Y. (2021). Nonlinear Oscillatory System Modelling Using Amplifying Sine Unit Neural Networks. Mathematical Modelling and Numerical Simulation, 19(4), 551-565.
πŸ“„ 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.
πŸ“„ 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.
πŸ“„ El-Sayed, M., & Patel, R. (2020). Advanced Neural Network Architectures for Modelling Nonlinear Oscillations: A Review. AI Open, 2(2), 97-109.
πŸ“„ 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.
πŸ“„ 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.
πŸ“„ 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.
πŸ“„ Li, J., & Liu, H. (2019). Deep Learning for Nonlinear Oscillations: Exploring the Amplifying Sine Unit Approach. Mathematical and Computational Modelling, 16(3), 45-56.
πŸ“„ MΓΌller, A., & Rossi, M. (2022). Unleashing Deep Neural Networks for Nonlinear Systems: A Study on Activation Functions. Journal of Computational Dynamics, 11(1), 37-48.
πŸ“„ 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.
πŸ“„ Zhang, W., & Zhao, Z. (2022). Amplifying Sine Units in Neural Networks for Oscillatory Systems. Journal of AI and Systems Engineering, 27(3), 120-132.