Fractional Dynamics Identification via Intelligent Unpacking of the Sample Autocovariance Function by Neural Networks
| Autor: | Grzegorz Sikora, Agnieszka Wyłomańska, Ireneusz Jablonski, Michał Balcerek, Dawid Szarek |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Anomalous diffusion
Computer science neural network fractional Brownian motion General Physics and Astronomy lcsh:Astrophysics 01 natural sciences Article 010305 fluids & plasmas Monte Carlo simulations symbols.namesake Robustness (computer science) anomalous diffusion 0103 physical sciences lcsh:QB460-466 010306 general physics lcsh:Science Gaussian process Fractional Brownian motion Artificial neural network estimation Function (mathematics) autocovariance function lcsh:QC1-999 Fractional dynamics Autocovariance symbols lcsh:Q Algorithm lcsh:Physics |
| Zdroj: | Entropy, Vol 22, Iss 1322, p 1322 (2020) Entropy Volume 22 Issue 11 |
| ISSN: | 1099-4300 |
| Popis: | Many single-particle tracking data related to the motion in crowded environments exhibit anomalous diffusion behavior. This phenomenon can be described by different theoretical models. In this paper, fractional Brownian motion (FBM) was examined as the exemplary Gaussian process with fractional dynamics. The autocovariance function (ACVF) is a function that determines completely the Gaussian process. In the case of experimental data with anomalous dynamics, the main problem is first to recognize the type of anomaly and then to reconstruct properly the physical rules governing such a phenomenon. The challenge is to identify the process from short trajectory inputs. Various approaches to address this problem can be found in the literature, e.g., theoretical properties of the sample ACVF for a given process. This method is effective however, it does not utilize all of the information contained in the sample ACVF for a given trajectory, i.e., only values of statistics for selected lags are used for identification. An evolution of this approach is proposed in this paper, where the process is determined based on the knowledge extracted from the ACVF. The designed method is intuitive and it uses information directly available in a new fashion. Moreover, the knowledge retrieval from the sample ACVF vector is enhanced with a learning-based scheme operating on the most informative subset of available lags, which is proven to be an effective encoder of the properties inherited in complex data. Finally, the robustness of the proposed algorithm for FBM is demonstrated with the use of Monte Carlo simulations. |
| Databáze: | OpenAIRE |
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