Identification of anomalous diffusion sources by unsupervised learning
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean-squared particle displacement following a power law 〈Δr^{2}〉∼t^{α}, where the diffusion exponent α characterizes whether the transport is subdiffusive (α<1...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.023248 |
| _version_ | 1797211439021162496 |
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| author | Raviteja Vangara Kim Ø. Rasmussen Dimiter N. Petsev Golan Bel Boian S. Alexandrov |
| author_facet | Raviteja Vangara Kim Ø. Rasmussen Dimiter N. Petsev Golan Bel Boian S. Alexandrov |
| author_sort | Raviteja Vangara |
| collection | DOAJ |
| description | Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean-squared particle displacement following a power law 〈Δr^{2}〉∼t^{α}, where the diffusion exponent α characterizes whether the transport is subdiffusive (α<1), diffusive (α=1), or superdiffusive (α>1). Due to the abundance of fBm processes in nature, significant efforts have been devoted to the identification and characterization of fBm sources in various phenomena. In practice, the identification of the fBm sources often relies on solving a complex and ill-posed inverse problem based on limited observed data. In the general case, the detected signals are formed by an unknown number of release sources, located at different locations and with different strengths, that act simultaneously. This means that the observed data are composed of mixtures of releases from an unknown number of sources, which makes the traditional inverse modeling approaches unreliable. Here, we report an unsupervised learning method, based on non-negative matrix factorization, that enables the identification of the unknown number of release sources as well the anomalous diffusion characteristics based on limited observed data and the general form of the corresponding fBm Green's function. We show that our method performs accurately for different types of sources and configurations with a predetermined number of sources with specific characteristics and introduced noise. |
| first_indexed | 2024-04-24T10:26:30Z |
| format | Article |
| id | doaj.art-ef46d722768f4240ab8a513696481e19 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:26:30Z |
| publishDate | 2020-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-ef46d722768f4240ab8a513696481e192024-04-12T16:54:43ZengAmerican Physical SocietyPhysical Review Research2643-15642020-05-012202324810.1103/PhysRevResearch.2.023248Identification of anomalous diffusion sources by unsupervised learningRaviteja VangaraKim Ø. RasmussenDimiter N. PetsevGolan BelBoian S. AlexandrovFractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean-squared particle displacement following a power law 〈Δr^{2}〉∼t^{α}, where the diffusion exponent α characterizes whether the transport is subdiffusive (α<1), diffusive (α=1), or superdiffusive (α>1). Due to the abundance of fBm processes in nature, significant efforts have been devoted to the identification and characterization of fBm sources in various phenomena. In practice, the identification of the fBm sources often relies on solving a complex and ill-posed inverse problem based on limited observed data. In the general case, the detected signals are formed by an unknown number of release sources, located at different locations and with different strengths, that act simultaneously. This means that the observed data are composed of mixtures of releases from an unknown number of sources, which makes the traditional inverse modeling approaches unreliable. Here, we report an unsupervised learning method, based on non-negative matrix factorization, that enables the identification of the unknown number of release sources as well the anomalous diffusion characteristics based on limited observed data and the general form of the corresponding fBm Green's function. We show that our method performs accurately for different types of sources and configurations with a predetermined number of sources with specific characteristics and introduced noise.http://doi.org/10.1103/PhysRevResearch.2.023248 |
| spellingShingle | Raviteja Vangara Kim Ø. Rasmussen Dimiter N. Petsev Golan Bel Boian S. Alexandrov Identification of anomalous diffusion sources by unsupervised learning Physical Review Research |
| title | Identification of anomalous diffusion sources by unsupervised learning |
| title_full | Identification of anomalous diffusion sources by unsupervised learning |
| title_fullStr | Identification of anomalous diffusion sources by unsupervised learning |
| title_full_unstemmed | Identification of anomalous diffusion sources by unsupervised learning |
| title_short | Identification of anomalous diffusion sources by unsupervised learning |
| title_sort | identification of anomalous diffusion sources by unsupervised learning |
| url | http://doi.org/10.1103/PhysRevResearch.2.023248 |
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