Learning dynamics from noisy observations

Abstract

We introduce a stable estimator for nonlinear systems observed through additive noise. The method separates model uncertainty from measurement uncertainty and remains accurate in the small-sample regime.

1. Method

Let x sub t denote the latent state and y sub t the measured value. The transition model is defined by

We estimate theta by minimizing the expected reconstruction loss with a smoothness penalty. Experiments on three benchmark systems show lower error than the deterministic baseline.