Simulation-Free Learning of GP-SDEs from Irregular Observations

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.

Machine Learning (cs.LG); Signal Processing (eess.SP); Machine Learning (stat.ML)

arXiv:2609.33112 [cs.LG]

(or arXiv:2609.33112v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.33112 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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