Physics Practical Magic

New research shows you can predict a system's future even if you have no idea what laws of physics are actually running it.

March 24, 2026

Original Paper

Predictability of Observables of Dynamical Systems

Xinyu Liu, Dongbin Xiu

arXiv · 2603.20641

The Takeaway

While science usually relies on physical models to forecast events, this paper shows that for many systems, a long enough history of observations contains a complete 'shadow' of the system's own rules. This allows for accurate predictions even if the underlying physics remains a complete mystery.

From the abstract

We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields a minimal order closure and an equivalent discrete delay representation of the observable dynamics. For nonlinear systems we introduce the notion of diminishing ambiguity, which provides a framework under which the instantaneous observable dynamics can be appr