# Early warning indicators via latent stochastic dynamical systems

arXiv: https://arxiv.org/abs/2309.03842 · HTML: https://mlsanity.com/paper/2309.03842/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 7 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning](https://mlsanity.com/paper/2106.09004/) (2021)
- [Learning Latent Dynamics for Partially-Observed Chaotic Systems](https://mlsanity.com/paper/1907.02452/) (2019)
- [Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space](https://mlsanity.com/paper/2204.12536/) (2022)
- [Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems](https://mlsanity.com/paper/2107.10127/) (2021)
- [An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable L'evy noise](https://mlsanity.com/paper/2201.13114/) (2022)
- [Integrated information as a common signature of dynamical and information-processing complexity](https://mlsanity.com/paper/2106.10211/) (2021)
- [Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles](https://mlsanity.com/paper/2205.00286/) (2022)
- [Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operator](https://mlsanity.com/paper/2304.11925/) (2023)
- [Learning effective dynamics from data-driven stochastic systems](https://mlsanity.com/paper/2205.04151/) (2022)

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

- [SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecasting](https://mlsanity.com/paper/2312.02646/) (2023)
- [Early warning prediction: Onsager-Machlup vs Schr"odinger](https://mlsanity.com/paper/2602.00143/) (2026)
- [Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport](https://mlsanity.com/paper/2603.15683/) (2026)

## Abstract (arXiv)

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliability. To this end, we develop a novel approach: the directed anisotropic diffusion map that captures the latent evolutionary dynamics in the low-dimensional manifold. Then three effective warning signals (Onsager-Machlup Indicator, Sample Entropy Indicator, and Transition Probability Indicator) are derived through the latent coordinates and the latent stochastic dynamical systems. To validate our framework, we apply this methodology to authentic electroencephalogram (EEG) data. We find that our early warning indicators are capable of detecting the tipping point during state transition. This framework not only bridges the latent dynamics with real-world data but also shows the potential ability for automatic labeling on complex high-dimensional time series.