Learning effective dynamics from data-driven stochastic systems
This work addresses the challenge of modeling multiscale stochastic dynamics in scientific and engineering applications, representing an incremental improvement with a new method for a known bottleneck.
The paper tackled the problem of learning effective dynamics from data-driven stochastic systems by proposing a novel algorithm, Auto-SDE, which accurately captures invariant slow manifolds from short-term observation data, as validated through numerical experiments.
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.