# Simulation-Free Learning of GP-SDEs from Irregular Observations

arXiv: https://arxiv.org/abs/2609.33112 · HTML: https://mlsanity.com/paper/2609.33112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching](https://mlsanity.com/paper/1807.05748/) (2018)
- [SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations](https://mlsanity.com/paper/2502.02472/) (2025)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs](https://mlsanity.com/paper/2312.10550/) (2023)
- [Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems](https://mlsanity.com/paper/2408.03330/) (2024)
- [Output-Dependent Gaussian Process State-Space Model](https://mlsanity.com/paper/2212.07608/) (2022)
- [Sequential Estimation of Gaussian Process-based Deep State-Space Models](https://mlsanity.com/paper/2301.12528/) (2023)
- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [SING: SDE Inference via Natural Gradients](https://mlsanity.com/paper/2506.17796/) (2025)
- [Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Models](https://mlsanity.com/paper/2309.01074/) (2023)
- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)

## Abstract (arXiv)

Gaussian process stochastic differential equations (GP-SDEs) provide a flexible Bayesian model for unknown continuous-time state dynamics with uncertainty quantification, but learning and inference from noisy and irregular observations remain computationally challenging. To address this issue, we propose GP-SDE Matching, a simulation-free variational framework for Bayesian GP drift learning and continuous-time state smoothing. We analytically marginalize the sparse GP posterior to derive a tractable drift-matching objective that accounts for both the posterior mean and uncertainty of the unknown drift. To handle irregular observations, we further introduce an irregular-time-aware variational state posterior that incorporates the actual observation times during both encoding and continuous-time marginal querying. Experiments on the stochastic Lorenz--63 system demonstrate substantially improved drift recovery and state reconstruction under irregular observations, while five system identification benchmarks show robust forecasting under increasing observation sparsity and competitive performance against existing latent-SDE and state-space methods.