Data-Based Reconstruction of Chaotic Systems by Stochastic Iterative Greedy Algorithm
It is challenging to reconstruct a nonlinear dynamical system when sufficient observations are not available. Recent study shows this problem can be solved by paradigm of compressive sensing. In this paper, we study the reconstruction of chaotic systems based on the stochastic gradient matching purs...
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| Veröffentlicht in: | Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-9 |
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| creator | Xiao, Yuzhu Song, Xueli Dong, Guoli |
| description | It is challenging to reconstruct a nonlinear dynamical system when sufficient observations are not available. Recent study shows this problem can be solved by paradigm of compressive sensing. In this paper, we study the reconstruction of chaotic systems based on the stochastic gradient matching pursuit (StoGradMP) method. Comparing with the previous method based on convex optimization, the study results show that the StoGradMP method performs much better when the numerical sampling period is small. So the present study enables potential application of the reconstruction method using limited observations in some special situations where limited observations can be acquired in limited time. |
| doi_str_mv | 10.1155/2020/6718304 |
| format | Article |
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Recent study shows this problem can be solved by paradigm of compressive sensing. In this paper, we study the reconstruction of chaotic systems based on the stochastic gradient matching pursuit (StoGradMP) method. Comparing with the previous method based on convex optimization, the study results show that the StoGradMP method performs much better when the numerical sampling period is small. So the present study enables potential application of the reconstruction method using limited observations in some special situations where limited observations can be acquired in limited time.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2020/6718304</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Algorithms ; Chaos theory ; Computational geometry ; Convex analysis ; Convexity ; Dynamical systems ; Greedy algorithms ; Iterative methods ; Matched pursuit ; Mathematical problems ; Methods ; Optimization ; Parameter identification ; Reconstruction ; Sparsity ; Success</subject><ispartof>Mathematical problems in engineering, 2020, Vol.2020 (2020), p.1-9</ispartof><rights>Copyright © 2020 Yuzhu Xiao et al.</rights><rights>Copyright © 2020 Yuzhu Xiao et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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| subjects | Algorithms Chaos theory Computational geometry Convex analysis Convexity Dynamical systems Greedy algorithms Iterative methods Matched pursuit Mathematical problems Methods Optimization Parameter identification Reconstruction Sparsity Success |
| title | Data-Based Reconstruction of Chaotic Systems by Stochastic Iterative Greedy Algorithm |
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