# Learning effective dynamics from data-driven stochastic systems

arXiv: https://arxiv.org/abs/2205.04151 · HTML: https://mlsanity.com/paper/2205.04151/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 9 May 2022.

## Builds on (most cited first, 7 of 7)

- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Deep learning to discover and predict dynamics on an inertial manifold](https://mlsanity.com/paper/2001.04263/) (2019)
- [Supervised Dimensionality Reduction for Big Data](https://mlsanity.com/paper/1709.01233/) (2017)
- [Kernel methods for center manifold approximation and a data-based version of the Center Manifold Theorem](https://mlsanity.com/paper/2012.00338/) (2020)
- [How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models](https://mlsanity.com/paper/2103.10264/) (2021)
- [Multiscale regression on unknown manifolds](https://mlsanity.com/paper/2101.05119/) (2021)
- [Predicting trajectory behaviour via machine-learned invariant manifolds](https://mlsanity.com/paper/2107.10154/) (2021)

## Built on by (most cited first, 3 of 3)

- [Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems](https://mlsanity.com/paper/2408.14821/) (2024)
- [Early warning indicators via latent stochastic dynamical systems](https://mlsanity.com/paper/2309.03842/) (2023)
- [Data driven modeling for self-similar dynamics](https://mlsanity.com/paper/2310.08282/) (2023)

## Abstract (arXiv)

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.