Recently, Gaussian processes have been utilized to model the vector field of
continuous dynamical systems. Bayesian inference for such models
\cite{hegde2022variational} has been extensively studied and has been applied
in tasks such as time series prediction, providing uncertain estimates.
However, previous Gaussian Process Ordinary Differential Equation (ODE) models
may underperform on datasets with non-Gaussian process priors, as their
constrained priors and mean-field posteriors may lack flexibility. To address
this limitation, we incorporate normalizing flows to reparameterize the vector
field of ODEs, resulting in a more flexible and expressive prior distribution.
Additionally, due to the analytically tractable probability density functions
of normalizing flows, we apply them to the posterior inference of GP ODEs,
generating a non-Gaussian posterior. Through these dual applications of
normalizing flows, our model improves accuracy and uncertainty estimates for
Bayesian Gaussian Process ODEs. The effectiveness of our approach is
demonstrated on simulated dynamical systems and real-world human motion data,
including tasks such as time series prediction and missing data recovery.
Experimental results indicate that our proposed method effectively captures
model uncertainty while improving accuracy