  Neural Stochastic Differential Equations model a dynamical environment with
neural nets assigned to their drift and diffusion terms. The high expressive
power of their nonlinearity comes at the expense of instability in the
identification of the large set of free parameters. This paper presents a
recipe to improve the prediction accuracy of such models in three steps: i)
accounting for epistemic uncertainty by assuming probabilistic weights, ii)
incorporation of partial knowledge on the state dynamics, and iii) training the
resultant hybrid model by an objective derived from a PAC-Bayesian
generalization bound. We observe in our experiments that this recipe
effectively translates partial and noisy prior knowledge into an improved model
fit.
