Learning effective dynamics from data-driven stochastic systems
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929195228069888 |
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| author | Feng, Lingyu Gao, Ting Dai, Min Duan, Jinqiao |
| author_facet | Feng, Lingyu Gao, Ting Dai, Min Duan, Jinqiao |
| contents | Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable and effective through numerical experiments under various evaluation metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04151 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Learning effective dynamics from data-driven stochastic systems Feng, Lingyu Gao, Ting Dai, Min Duan, Jinqiao Machine Learning Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable and effective through numerical experiments under various evaluation metrics. |
| title | Learning effective dynamics from data-driven stochastic systems |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2205.04151 |