# Variational Deep Learning for the Identification and Reconstruction of Chaotic and Stochastic Dynamical Systems from Noisy and Partial Observations

arXiv: https://arxiv.org/abs/2009.02296 · HTML: https://mlsanity.com/paper/2009.02296/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2020.

## Built on by (most cited first, 8 of 8)

- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Reverse engineering recurrent neural networks with Jacobian switching linear dynamical systems](https://mlsanity.com/paper/2111.01256/) (2021)
- [Learning stochastic dynamical systems with neural networks mimicking the Euler-Maruyama scheme](https://mlsanity.com/paper/2105.08449/) (2021)
- [HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equations](https://mlsanity.com/paper/2310.04832/) (2023)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)
- [Learning Space-Time Continuous Neural PDEs from Partially Observed States](https://mlsanity.com/paper/2307.04110/) (2023)
- [STEADY: Simultaneous State Estimation and Dynamics Learning from Indirect Observations](https://mlsanity.com/paper/2203.01299/) (2022)
- [Reinforcement learning based data assimilation for unknown state model](https://mlsanity.com/paper/2511.02286/) (2025)

## Abstract (arXiv)

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial observations. Here, we address this challenge and investigate variational deep learning schemes. Within the proposed framework, we jointly learn an inference model to reconstruct the true states of the system and the governing laws of these states from series of noisy and partial data. In doing so, this framework bridges classical data assimilation and state-of-the-art machine learning techniques. We also demonstrate that it generalises state-of-the-art methods. Importantly, both the inference model and the governing model embed stochastic components to account for stochastic variabilities, model errors, and reconstruction uncertainties. Various experiments on chaotic and stochastic dynamical systems support the relevance of our scheme w.r.t. state-of-the-art approaches.