Simulation-Free Learning of GP-SDEs from Irregular Observations

2026-09-27

AI Summary

This study addresses the computational complexity of inference in Gaussian Process Stochastic Differential Equations (GP-SDEs) under irregularly sampled noisy observations by proposing the GP-SDE Matching framework. Methodologically, it achieves simulation-free variational Bayesian drift learning and state smoothing through the analytical marginalization of sparse Gaussian process posteriors. Furthermore, a drift matching objective that jointly accounts for both mean estimates and uncertainty is derived, complemented by an irregular-time-aware variational state posterior. Experimental evaluations demonstrate that the proposed approach significantly enhances drift recovery accuracy on the Lorenz-63 system and exhibits superior predictive robustness compared to existing methods across standard benchmarks.

Abstract

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.

Problem

• Gaussian process stochastic differential equations
• irregular observations
• Bayesian inference
• computational challenge
• state dynamics

Innovation

• Simulation-Free Learning
• GP-SDEs
• Variational Framework
• Irregular Observations
• Drift Matching