-
Previous Article
An integrated approach for the operations of distribution and lateral transshipment for seasonal products - A case study in household product industry
- JIMO Home
- This Issue
-
Next Article
Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method
Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm
1. | Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China |
2. | Department of Mathematics, Cleveland State University, Cleveland, OH 44115, United States |
References:
[1] |
A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence, IEEE Transcations on Neural Networks, 11 (2000), 697-709.
doi: 10.1109/72.846741. |
[2] |
Y. Fang and T. W. S. Chow, Non-linear dynamical systems control using a new RNN temporal learning strategy, IEEE Trans on Circuit and Systems, Part II, 52 (2005), 719-723. |
[3] |
R. A. Conn, K. Scheinberg and N. L. Vicente, "Introduction to Derivative-free Optimization," SIAM, 2009.
doi: 10.1137/1.9780898718768. |
[4] |
J. F. G. Freitas, M. Niranjan, A. H. Gee and A. Doucet, Sequential Monte Carlo methods to train neural network models, Neural Computation, 12 (2000), 955-993.
doi: 10.1162/089976600300015664. |
[5] |
L. K. Li, Learning sunspot series dynamics by recurrent neural networks, in "Advances in Data Mining and Modeling" (eds. W. K. Ching and K. P. Ng), World Science, (2003), 107-115.
doi: 10.1142/9789812704955_0009. |
[6] |
L. K. Li, W. K. Pang, W. T. Yu and M. D. Trout, Forecasting short-term exchange Rates: a recurrent neural network approach, in "Neural Networks in Business Forecasting" (eds. G. P. Zhang), Idea Group Publishing, (2004), 195-212.
doi: 10.4018/9781591401766.ch010. |
[7] |
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations, International Journal of Pure and Applied Mathematics, 39 (2007), 545-562. |
[8] |
L. K. Li and S. Shao, A neural network approach for global optimization with applications, Neural Network World, 18 (2008), 365-379. |
[9] |
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the short-term foreign exchange rates, Applied Mathematical Sciences, 2 (2008), 1705-1728. |
[10] |
X. D. Li, J. K. L. Ho and T. W. S. Chow, Approximation of dynamical time-variant systems by continuous-time recurrent neural networks, IEEE Trans on Circuit and Systems, Part II, 52 (2005), 656-660. |
[11] |
X. B. Liang and J. Wang, A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints, IEEE Transactions on Neural Networks, 11 (2000), 1251-1262.
doi: 10.1109/72.883412. |
[12] |
Z. Liu and I. Elhanany, A Fast and Scalable Recurrent Neural Network Based on Stochastic Meta Descent, IEEE Transactions on Neural Networks, 19 (2008), 1652-1658.
doi: 10.1109/TNN.2008.2000838. |
[13] |
S. Wang, Q. Shao and X. Zhou, Knot-optimizing spline networks (KOSNETS) for nonparametric regression, Journal of Industrial and Management Optimization, 4 (2008), 33?52. |
[14] |
X. Wang and E. K. Blum, Discrete-time versus continuous-time models of neural networks, Journal of Computer and System Sciences, 45 (1992), 1-19.
doi: 10.1016/0022-0000(92)90038-K. |
[15] |
R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks, Neural Computation, 1 (1989), 270-280.
doi: 10.1162/neco.1989.1.2.270. |
[16] |
L. Xu and W. Liu, A new recurrent neural network adaptive approach for host-gate way rate control protocol within intranets using ATM ABR service, Journal of Industrial and Management Optimization, 1 (2005), 389-404. |
[17] |
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex, Neural Computation, 34 (2000), 79-98. |
[18] |
K. F. C. Yiu, S. Wang, K. L. Teo and A. H. Tsoi, Nonlinear system modeling via knot-optimizing B-spline networks, IEEE Transactions on Neural Networks, 12 (2001), 1013-1022.
doi: 10.1109/72.950131. |
[19] |
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization, Journal of Global Optimization, 28 (2004), 229-238.
doi: 10.1023/B:JOGO.0000015313.93974.b0. |
show all references
References:
[1] |
A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence, IEEE Transcations on Neural Networks, 11 (2000), 697-709.
doi: 10.1109/72.846741. |
[2] |
Y. Fang and T. W. S. Chow, Non-linear dynamical systems control using a new RNN temporal learning strategy, IEEE Trans on Circuit and Systems, Part II, 52 (2005), 719-723. |
[3] |
R. A. Conn, K. Scheinberg and N. L. Vicente, "Introduction to Derivative-free Optimization," SIAM, 2009.
doi: 10.1137/1.9780898718768. |
[4] |
J. F. G. Freitas, M. Niranjan, A. H. Gee and A. Doucet, Sequential Monte Carlo methods to train neural network models, Neural Computation, 12 (2000), 955-993.
doi: 10.1162/089976600300015664. |
[5] |
L. K. Li, Learning sunspot series dynamics by recurrent neural networks, in "Advances in Data Mining and Modeling" (eds. W. K. Ching and K. P. Ng), World Science, (2003), 107-115.
doi: 10.1142/9789812704955_0009. |
[6] |
L. K. Li, W. K. Pang, W. T. Yu and M. D. Trout, Forecasting short-term exchange Rates: a recurrent neural network approach, in "Neural Networks in Business Forecasting" (eds. G. P. Zhang), Idea Group Publishing, (2004), 195-212.
doi: 10.4018/9781591401766.ch010. |
[7] |
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations, International Journal of Pure and Applied Mathematics, 39 (2007), 545-562. |
[8] |
L. K. Li and S. Shao, A neural network approach for global optimization with applications, Neural Network World, 18 (2008), 365-379. |
[9] |
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the short-term foreign exchange rates, Applied Mathematical Sciences, 2 (2008), 1705-1728. |
[10] |
X. D. Li, J. K. L. Ho and T. W. S. Chow, Approximation of dynamical time-variant systems by continuous-time recurrent neural networks, IEEE Trans on Circuit and Systems, Part II, 52 (2005), 656-660. |
[11] |
X. B. Liang and J. Wang, A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints, IEEE Transactions on Neural Networks, 11 (2000), 1251-1262.
doi: 10.1109/72.883412. |
[12] |
Z. Liu and I. Elhanany, A Fast and Scalable Recurrent Neural Network Based on Stochastic Meta Descent, IEEE Transactions on Neural Networks, 19 (2008), 1652-1658.
doi: 10.1109/TNN.2008.2000838. |
[13] |
S. Wang, Q. Shao and X. Zhou, Knot-optimizing spline networks (KOSNETS) for nonparametric regression, Journal of Industrial and Management Optimization, 4 (2008), 33?52. |
[14] |
X. Wang and E. K. Blum, Discrete-time versus continuous-time models of neural networks, Journal of Computer and System Sciences, 45 (1992), 1-19.
doi: 10.1016/0022-0000(92)90038-K. |
[15] |
R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks, Neural Computation, 1 (1989), 270-280.
doi: 10.1162/neco.1989.1.2.270. |
[16] |
L. Xu and W. Liu, A new recurrent neural network adaptive approach for host-gate way rate control protocol within intranets using ATM ABR service, Journal of Industrial and Management Optimization, 1 (2005), 389-404. |
[17] |
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex, Neural Computation, 34 (2000), 79-98. |
[18] |
K. F. C. Yiu, S. Wang, K. L. Teo and A. H. Tsoi, Nonlinear system modeling via knot-optimizing B-spline networks, IEEE Transactions on Neural Networks, 12 (2001), 1013-1022.
doi: 10.1109/72.950131. |
[19] |
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization, Journal of Global Optimization, 28 (2004), 229-238.
doi: 10.1023/B:JOGO.0000015313.93974.b0. |
[1] |
Leong-Kwan Li, Sally Shao. Convergence analysis of the weighted state space search algorithm for recurrent neural networks. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 193-207. doi: 10.3934/naco.2014.4.193 |
[2] |
K. L. Mak, J. G. Peng, Z. B. Xu, K. F. C. Yiu. A novel neural network for associative memory via dynamical systems. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 573-590. doi: 10.3934/dcdsb.2006.6.573 |
[3] |
Lixin Xu, Wanquan Liu. A new recurrent neural network adaptive approach for host-gate way rate control protocol within intranets using ATM ABR service. Journal of Industrial and Management Optimization, 2005, 1 (3) : 389-404. doi: 10.3934/jimo.2005.1.389 |
[4] |
Sanjay K. Mazumdar, Cheng-Chew Lim. A neural network based anti-skid brake system. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 321-338. doi: 10.3934/dcds.1999.5.321 |
[5] |
Léo Bois, Emmanuel Franck, Laurent Navoret, Vincent Vigon. A neural network closure for the Euler-Poisson system based on kinetic simulations. Kinetic and Related Models, 2022, 15 (1) : 49-89. doi: 10.3934/krm.2021044 |
[6] |
Meiyu Sui, Yejuan Wang, Peter E. Kloeden. Pullback attractors for stochastic recurrent neural networks with discrete and distributed delays. Electronic Research Archive, 2021, 29 (2) : 2187-2221. doi: 10.3934/era.2020112 |
[7] |
Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure and Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655 |
[8] |
Yang Mi, Kang Zheng, Song Wang. Homography estimation along short videos by recurrent convolutional regression network. Mathematical Foundations of Computing, 2020, 3 (2) : 125-140. doi: 10.3934/mfc.2020014 |
[9] |
Thi Tuyet Trang Chau, Pierre Ailliot, Valérie Monbet, Pierre Tandeo. Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022054 |
[10] |
Vena Pearl Bongolan-walsh, David Cheban, Jinqiao Duan. Recurrent motions in the nonautonomous Navier-Stokes system. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 255-262. doi: 10.3934/dcdsb.2003.3.255 |
[11] |
Ndolane Sene. Fractional input stability and its application to neural network. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 853-865. doi: 10.3934/dcdss.2020049 |
[12] |
Ying Sue Huang, Chai Wah Wu. Stability of cellular neural network with small delays. Conference Publications, 2005, 2005 (Special) : 420-426. doi: 10.3934/proc.2005.2005.420 |
[13] |
King Hann Lim, Hong Hui Tan, Hendra G. Harno. Approximate greatest descent in neural network optimization. Numerical Algebra, Control and Optimization, 2018, 8 (3) : 327-336. doi: 10.3934/naco.2018021 |
[14] |
Shyan-Shiou Chen, Chih-Wen Shih. Asymptotic behaviors in a transiently chaotic neural network. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 805-826. doi: 10.3934/dcds.2004.10.805 |
[15] |
Zhigang Zeng, Tingwen Huang. New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays. Journal of Industrial and Management Optimization, 2011, 7 (2) : 283-289. doi: 10.3934/jimo.2011.7.283 |
[16] |
John R. Tucker. Attractors and kernels: Linking nonlinear PDE semigroups to harmonic analysis state-space decomposition. Conference Publications, 2001, 2001 (Special) : 366-370. doi: 10.3934/proc.2001.2001.366 |
[17] |
Irena Pawłow, Wojciech M. Zajączkowski. Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm. Discrete and Continuous Dynamical Systems - S, 2011, 4 (2) : 441-466. doi: 10.3934/dcdss.2011.4.441 |
[18] |
Mo Chen. Recurrent solutions of the Schrödinger-KdV system with boundary forces. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 5149-5170. doi: 10.3934/dcdsb.2020337 |
[19] |
Fred C. Pinto. Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 117-136. doi: 10.3934/dcds.1999.5.117 |
[20] |
Karl Peter Hadeler. Structured populations with diffusion in state space. Mathematical Biosciences & Engineering, 2010, 7 (1) : 37-49. doi: 10.3934/mbe.2010.7.37 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]