# Learning interpretable continuous-time models of latent stochastic dynamical systems

arXiv: https://arxiv.org/abs/1902.04420 · HTML: https://mlsanity.com/paper/1902.04420/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2019.

## Built on by (most cited first, 30 of 30)

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- [Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems](https://mlsanity.com/paper/2408.03330/) (2024)
- [Self-supervised contrastive learning performs non-linear system identification](https://mlsanity.com/paper/2410.14673/) (2024)
- [Free-Form Variational Inference for Gaussian Process State-Space Models](https://mlsanity.com/paper/2302.09921/) (2023)
- [In-Context Learning of Stochastic Differential Equations with Foundation Inference Models](https://mlsanity.com/paper/2502.19049/) (2025)
- [Moment-Based Variational Inference for Stochastic Differential Equations](https://mlsanity.com/paper/2103.00988/) (2021)
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- [Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting](https://mlsanity.com/paper/2106.11712/) (2021)
- [Deep inference of latent dynamics with spatio-temporal super-resolution using selective backpropagation through time](https://mlsanity.com/paper/2111.00070/) (2021)
- [Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs](https://mlsanity.com/paper/2205.11894/) (2022)
- [SING: SDE Inference via Natural Gradients](https://mlsanity.com/paper/2506.17796/) (2025)
- [Generative Modeling of Neural Dynamics via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2412.12112/) (2024)
- [Mesoscopic modeling of hidden spiking neurons](https://mlsanity.com/paper/2205.13493/) (2022)
- [Trainability, Expressivity and Interpretability in Gated Neural ODEs](https://mlsanity.com/paper/2307.06398/) (2023)
- [Inferring Inference](https://mlsanity.com/paper/2310.03186/) (2023)
- [Finding separatrices of dynamical flows with Deep Koopman Eigenfunctions](https://mlsanity.com/paper/2505.15231/) (2025)
- [Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models](https://mlsanity.com/paper/2510.12618/) (2025)
- [Neural Diffusion Intensity Models for Point Process Data](https://mlsanity.com/paper/2602.24083/) (2026)
- [Modeling Nonlinear Dynamics in Continuous Time with Inductive Biases on Decay Rates and/or Frequencies](https://mlsanity.com/paper/2212.13033/) (2022)
- [A projected nonlinear state-space model for forecasting time series signals](https://mlsanity.com/paper/2311.13247/) (2023)
- [Langevin Flows for Modeling Neural Latent Dynamics](https://mlsanity.com/paper/2507.11531/) (2025)
- [Towards Foundation Inference Models that Learn ODEs In-Context](https://mlsanity.com/paper/2510.12650/) (2025)
- [Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems](https://mlsanity.com/paper/2606.14079/) (2026)
- [Simulation-Free Learning of GP-SDEs from Irregular Observations](https://mlsanity.com/paper/2609.33112/) (2026)
- [Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginals](https://mlsanity.com/paper/2610.04390/) (2026)

## Abstract (arXiv)

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolution function drawn from a Gaussian process (GP) conditioned on a set of learnt fixed points and corresponding local Jacobian matrices. This form yields a flexible nonparametric model of the dynamics, with a representation corresponding directly to the interpretable portraits routinely employed in the study of nonlinear dynamical systems. The learning algorithm combines inference of continuous latent paths underlying observed data with a sparse variational description of the dynamical process. We demonstrate our approach on simulated data from different nonlinear dynamical systems.