# Learning Latent Dynamics for Partially-Observed Chaotic Systems

arXiv: https://arxiv.org/abs/1907.02452 · HTML: https://mlsanity.com/paper/1907.02452/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2019.

## Built on by (most cited first, 18 of 18)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Discovering Sparse Interpretable Dynamics from Partial Observations](https://mlsanity.com/paper/2107.10879/) (2021)
- [Deep learning delay coordinate dynamics for chaotic attractors from partial observable data](https://mlsanity.com/paper/2211.11061/) (2022)
- [Reconstruction, forecasting, and stability of chaotic dynamics from partial data](https://mlsanity.com/paper/2305.15111/) (2023)
- [Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks](https://mlsanity.com/paper/2111.06447/) (2021)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)
- [Online Calibration of Deep Learning Sub-Models for Hybrid Numerical Modeling Systems](https://mlsanity.com/paper/2311.10665/) (2023)
- [Learning Absorption Rates in Glucose-Insulin Dynamics from Meal Covariates](https://mlsanity.com/paper/2304.14300/) (2023)
- [Early warning indicators via latent stochastic dynamical systems](https://mlsanity.com/paper/2309.03842/) (2023)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)
- [Reconstructing a dynamical system and forecasting time series by self-consistent deep learning](https://mlsanity.com/paper/2108.01862/) (2021)
- [Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics](https://mlsanity.com/paper/2211.11580/) (2022)
- [Characterizing control between interacting subsystems with deep Jacobian estimation](https://mlsanity.com/paper/2507.01946/) (2025)
- [Ensemble forecasts in reproducing kernel Hilbert space family](https://mlsanity.com/paper/2207.14653/) (2022)
- [Dynamic Structure Estimation from Bandit Feedback using Nonvanishing Exponential Sums](https://mlsanity.com/paper/2206.00861/) (2022)
- [Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series](https://mlsanity.com/paper/2306.16593/) (2023)
- [Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism](https://mlsanity.com/paper/2609.34566/) (2026)

## Abstract (arXiv)

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications, including long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly learn an ODE (Ordinary Differential Equation) representation in the latent space and reconstructing latent states. Through numerical experiments, we demonstrate the relevance of the proposed framework w.r.t. state-of-the-art approaches in terms of short-term forecasting performance and long-term behaviour. We further discuss how the proposed framework relates to Koopman operator theory and Takens' embedding theorem.