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Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing
Open accessAbstract
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
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Cites
An Introduction To Compressive Sampling
Candes, E. J., & Wakin, M. B. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914731 · Cited by 10,017
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Data-driven discovery of partial differential equations
Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017) · Science Advances · doi:10.1126/sciadv.1602614 · Cited by 1,557
Data-driven discovery of coordinates and governing equations
Champion, K., Lusch, B., Kutz, J. N., & Brunton, S. L. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1906995116 · Cited by 909
Chaos as an intermittently forced linear system
Brunton, S. L., Brunton, B. W., Proctor, J. L., Kaiser, E., & Kutz, J. N. (2017) · Nature Communications · doi:10.1038/s41467-017-00030-8 · Cited by 608
Inferring biological networks by sparse identification of nonlinear dynamics
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Metadata
- Authors
- Wang, W.-X., Yang, R., Lai, Y.-C., Kovanis, V., & Grebogi, C.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2011-04-15
- Volume
- 106
- Issue
- 15
- Pages
- 154101-154101
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2137258853
- Cited by
- 352
- References
- 1
- FWCI
- 12.70
- Type
- journal article
- Language
- en
- Open access
- green
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- Wang, W.-X., Yang, R., Lai, Y.-C., Kovanis, V., & Grebogi, C. (2011). Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing. Physical Review Letters. https://doi.org/10.1103/physrevlett.106.154101
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