The paper addresses systems where slow-moving variables (like weather patterns) are influenced by fast-moving unobserved processes (like molecular dynamics). When you only observe the slow variables along a single trajectory, learning the underlying dynamics is hard. The authors use stochastic averaging to reduce the full multiscale model to an effective model for just the slow variables, then train a normalizing flow (a flexible neural density model) to learn the invariant distribution of the fast process that's needed for the reduction. They optimize this end-to-end using the likelihood of the observed slow trajectory and add Bayesian uncertainty quantification via variational inference.
Main takeaways:
- Tackles learning dynamics when you see only slow variables but fast hidden processes influence them
- Uses principled stochastic averaging instead of generic dimensionality reduction like PCA, respecting the dynamical structure
- Normalizing flows parameterize the unknown invariant distribution of the fast (unobserved) variables
- End-to-end training optimizes a penalized likelihood objective derived from the reduced dynamics
- Includes Bayesian uncertainty quantification using a second normalizing flow for the posterior