# Learning Continuous-Time Dynamics by Stochastic Differential Networks

arXiv: https://arxiv.org/abs/2006.06145 · HTML: https://mlsanity.com/paper/2006.06145/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

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

- [Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2301.11308/) (2023)
- [Decoupled Drift-Diffusion World Models for Consistent Future Frame Prediction](https://mlsanity.com/paper/2610.19212/) (2026)

## Abstract (arXiv)

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and observed data are high-dimensional, it is generally impossible to derive a precise continuous-time stochastic process to describe the system behaviors. To solve the above problem, we apply Variational Bayesian method and propose a flexible continuous-time stochastic recurrent neural network named Variational Stochastic Differential Networks (VSDN), which embeds the complicated dynamics of the sporadic time series by neural Stochastic Differential Equations (SDE). VSDNs capture the stochastic dependency among latent states and observations by deep neural networks. We also incorporate two differential Evidence Lower Bounds to efficiently train the models. Through comprehensive experiments, we show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and interpolation tasks for sporadic time series.