# Deep Generative Modeling for Identification of Noisy, Non-Stationary Dynamical Systems

arXiv: https://arxiv.org/abs/2410.02079 · HTML: https://mlsanity.com/paper/2410.02079/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 58 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Learning Stochastic Recurrent Networks](https://mlsanity.com/paper/1411.7610/) (2014)
- [Z-Forcing: Training Stochastic Recurrent Networks](https://mlsanity.com/paper/1711.05411/) (2017)
- [A variance modeling framework based on variational autoencoders for speech enhancement](https://mlsanity.com/paper/1902.01605/) (2019)
- [HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equations](https://mlsanity.com/paper/2310.04832/) (2023)
- [Nonlinear control in the nematode C. elegans](https://mlsanity.com/paper/2001.08332/) (2020)

## Built on by (most cited first, 2 of 2)

- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis](https://mlsanity.com/paper/2503.01036/) (2025)

## Abstract (arXiv)

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary differential equation (ODE) models for nonlinear, noisy, and non-autonomous dynamical systems and propose a machine learning method for data-driven system identification. While many methods tackle noisy and limited data, non-stationarity - where differential equation parameters change over time - has received less attention. Our method, dynamic SINDy, combines variational inference with SINDy (sparse identification of nonlinear dynamics) to model time-varying coefficients of sparse ODEs. This framework allows for uncertainty quantification of ODE coefficients, expanding on previous methods for autonomous systems. These coefficients are then interpreted as latent variables and added to the system to obtain an autonomous dynamical model. We validate our approach using synthetic data, including nonlinear oscillators and the Lorenz system, and apply it to neuronal activity data from C. elegans. Dynamic SINDy uncovers a global nonlinear model, showing it can handle real, noisy, and chaotic datasets. We aim to apply our method to a variety of problems, specifically dynamic systems with complex time-dependent parameters.