An end-to-end deep learning approach for extracting stochastic dynamical systems with $\alpha$-stable L\'evy noise
| Autor: | Fang, Cheng, Lu, Yubin, Gao, Ting, Duan, Jinqiao |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/5.0089832 |
| Popis: | Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical systems to stochastic dynamical systems, especially those driven by non-Gaussian multiplicative noise. However, lots of log-likelihood based algorithms that work well for Gaussian cases cannot be directly extended to non-Gaussian scenarios which could have high error and low convergence issues. In this work, we overcome some of these challenges and identify stochastic dynamical systems driven by $\alpha$-stable L\'evy noise from only random pairwise data. Our innovations include: (1) designing a deep learning approach to learn both drift and diffusion coefficients for L\'evy induced noise with $\alpha$ across all values, (2) learning complex multiplicative noise without restrictions on small noise intensity, (3) proposing an end-to-end complete framework for stochastic systems identification under a general input data assumption, that is, $\alpha$-stable random variable. Finally, numerical experiments and comparisons with the non-local Kramers-Moyal formulas with moment generating function confirm the effectiveness of our method. Comment: 26 pages,15 figures |
| Databáze: | arXiv |
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