Learning effective dynamics from data-driven stochastic systems

• URL: http://arxiv.org/abs/2205.04151v3
• Date: Sat, 30 Dec 2023 03:27:49 GMT
• Title: Learning effective dynamics from data-driven stochastic systems
• Authors: Lingyu Feng, Ting Gao, Min Dai and Jinqiao Duan
• Abstract summary: This work is devoted to investigating the effective dynamics for slow-fast dynamical systems. We propose a novel algorithm including a neural network called Auto-SDE to learn in slow manifold.
• Score: 2.4578723416255754
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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