Abstract

Hod Lipson: Active Learning of Dynamical Systems

This talk will present processes for learning dynamical systems. Complex nonlinear dynamics arise in many fields of science and engineering, but automatically uncovering the underlying differential equations directly from observations poses a challenging machine-learning task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate sets of symbolic equations for a dynamical systems directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the time series of all variables are observable (possibly with some noise). Previous automated symbolic modeling approaches of coupled physical systems produced a linear or require a nonlinear model to be provided manually. We use an active-learning process that interrogates and models each (possibly coupled) variable separately, by intelligently perturbing and destabilizing the system in order to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated "reverse engineering" approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively complex systems in the future.