# Identifying Latent Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2007.06075 · HTML: https://mlsanity.com/paper/2007.06075/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2020.

## Built on by (most cited first, 21 of 21)

- [Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning](https://mlsanity.com/paper/2106.09004/) (2021)
- [Latent SDEs on Homogeneous Spaces](https://mlsanity.com/paper/2306.16248/) (2023)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equations](https://mlsanity.com/paper/2310.04832/) (2023)
- [Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles](https://mlsanity.com/paper/2205.00286/) (2022)
- [From latent dynamics to meaningful representations](https://mlsanity.com/paper/2209.00905/) (2022)
- [SING: SDE Inference via Natural Gradients](https://mlsanity.com/paper/2506.17796/) (2025)
- [Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes](https://mlsanity.com/paper/2404.09402/) (2024)
- [Generative Modeling of Neural Dynamics via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2412.12112/) (2024)
- [Compositional Law Parsing with Latent Random Functions](https://mlsanity.com/paper/2209.09115/) (2022)
- [Latent Neural Stochastic Differential Equations for Change Point Detection](https://mlsanity.com/paper/2208.10317/) (2022)
- [Neural Stochastic Differential Equations with Change Points: A Generative Adversarial Approach](https://mlsanity.com/paper/2312.13152/) (2023)
- [Geometric regularization of autoencoders via observed stochastic dynamics](https://mlsanity.com/paper/2604.16282/) (2026)
- [Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling](https://mlsanity.com/paper/2311.00797/) (2023)
- [Variational Neural Stochastic Differential Equations with Change Points](https://mlsanity.com/paper/2411.00635/) (2024)
- [Stochastic Optimal Control for Continuous-Time fMRI Representation Learning](https://mlsanity.com/paper/2502.04892/) (2025)
- [Neural Langevin Dynamics: towards interpretable Neural Stochastic Differential Equations](https://mlsanity.com/paper/2211.09537/) (2022)
- [Discovering mesoscopic descriptions of collective movement with neural stochastic modelling](https://mlsanity.com/paper/2303.09906/) (2023)
- [Improving the Noise Estimation of Latent Neural Stochastic Differential Equations](https://mlsanity.com/paper/2412.17499/) (2024)
- [Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems](https://mlsanity.com/paper/2606.14079/) (2026)
- [Continuous-Time Trajectory Generation from Discrete Observations with Stochasticity](https://mlsanity.com/paper/2609.32026/) (2026)

## Abstract (arXiv)

We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown Ito process, the proposed method learns the mapping from ambient to latent space, and the underlying SDE coefficients, through a self-supervised learning approach. Using the framework of variational autoencoders, we consider a conditional generative model for the data based on the Euler-Maruyama approximation of SDE solutions. Furthermore, we use recent results on identifiability of latent variable models to show that the proposed model can recover not only the underlying SDE coefficients, but also the original latent variables, up to an isometry, in the limit of infinite data. We validate the method through several simulated video processing tasks, where the underlying SDE is known, and through real world datasets.