Learning Partially Known Stochastic Dynamics with Empirical PAC Bayes
This work addresses parameter instability in neural stochastic dynamics models, which is an incremental improvement for applications requiring robust dynamical system modeling.
The paper tackles the instability in identifying parameters of Neural Stochastic Differential Equations by incorporating partial prior knowledge and epistemic uncertainty through a PAC-Bayesian training objective, resulting in improved model fit as demonstrated in experiments.
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.