Bayesian Gaussian Process ODEs via Double Normalizing Flows
Published in Proceedings of the 28th International Conference on Artificial Intelligence and Statistics (AISTATS 2025), 2025
Standard GP-ODEs use a Gaussian process vector field with an RBF kernel, limiting expressiveness on complex dynamics. We introduce normalizing flows in two places — to reparameterise the ODE vector field (a data-driven prior) and to enrich the inducing-variable posterior (a non-mean-field approximation). The analytically tractable density of planar flows makes both transformations compatible with variational inference. Validated on simulated dynamical systems and CMU MoCap with improved accuracy and uncertainty calibration over GP-ODE / npODE / ODE2VAE / Latent SDE.
Recommended citation: Xu, J., Du, S., Yang, J., Ding, X., Zeng, D. and Paisley, J. (2025). Bayesian Gaussian Process ODEs via Double Normalizing Flows. AISTATS 2025, PMLR 258, pp.235-243.
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