  Homeostasis, the ability to maintain a stable internal environment in the
face of perturbations, is essential for the functioning of living systems.
Given observations of a system, or even a detailed model of one, it is both
valuable and extremely challenging to extract the control objectives of the
homeostatic mechanisms. Lacking a clear separation between plant and
controller, frameworks such as inverse optimal control and inverse
reinforcement learning are unable to identify the homeostatic mechanisms. A
recently developed data-driven algorithm, Identifying Regulation with
Adversarial Surrogates (IRAS), detects highly regulated or conserved quantities
as the solution of a min-max optimization scheme that automates classical
surrogate data methods. Yet, the definition of homeostasis as regulation within
narrow limits is too strict for biological systems which show sustained
oscillations such as circadian rhythms. In this work, we introduce Identifying
Dynamic Regulation with Adversarial Surrogates (IDRAS), a generalization of the
IRAS algorithm, capable of identifying control objectives that are regulated
with respect to a dynamical reference value. We test the algorithm on
simulation data from realistic biological models and benchmark physical
systems, demonstrating excellent empirical results.
