# Sparse Identification of Slow Timescale Dynamics

arXiv: https://arxiv.org/abs/2006.00940 · HTML: https://mlsanity.com/paper/2006.00940/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [Benchmarking sparse system identification with low-dimensional chaos](https://mlsanity.com/paper/2302.10787/) (2023)
- [Coarse-Graining Hamiltonian Systems Using WSINDy](https://mlsanity.com/paper/2310.05879/) (2023)
- [Deep Learning of Conjugate Mappings](https://mlsanity.com/paper/2104.01874/) (2021)
- [Discover governing differential equations from evolving systems](https://mlsanity.com/paper/2301.07863/) (2023)
- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulations](https://mlsanity.com/paper/2311.05961/) (2023)
- [Double projection for reconstructing dynamical systems: between stochastic and deterministic regimes](https://mlsanity.com/paper/2510.01089/) (2025)
- [Real-Time Motion Detection Using Dynamic Mode Decomposition](https://mlsanity.com/paper/2405.05057/) (2024)
- [Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps](https://mlsanity.com/paper/2407.00011/) (2024)
- [Impilict Runge-Kutta based sparse identification of governing equations in biologically motivated systems](https://mlsanity.com/paper/2502.20319/) (2025)

## Abstract (arXiv)

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the emergent slow scale evolution is unknown. Yet the course-grained, slow scale dynamics is often of greatest interest in practice. In this work we present an accurate and efficient method for extracting the slow timescale dynamics from signals exhibiting multiple timescales that are amenable to averaging. The method relies on tracking the signal at evenly-spaced intervals with length given by the period of the fast timescale, which is discovered using clustering techniques in conjunction with the dynamic mode decomposition. Sparse regression techniques are then used to discover a mapping which describes iterations from one data point to the next. We show that for sufficiently disparate timescales this discovered mapping can be used to discover the continuous-time slow dynamics, thus providing a novel tool for extracting dynamics on multiple timescales.