  Thermodynamic irreversibility is a crucial property of living matter.
Irreversible processes maintain spatiotemporally complex structures and
functions characteristic of living systems. In high-dimensional biological
dynamics, robust and general quantification of irreversibility remains a
challenging task due to experimental noise and nonlinear interactions coupling
many degrees of freedom. Here we use deep learning to identify tractable,
low-dimensional representations of phase-field patterns in a canonical protein
signaling process -- the Rho-GTPase system -- as well as complex
Ginzburg-Landau dynamics. We show that factorizing variational autoencoder
neural networks learn informative pattern features robustly to noise. Resulting
neural-network representations reveal signatures of mesoscopic broken detailed
balance and time-reversal asymmetry in Rho-GTPase and complex Ginzburg-Landau
wave dynamics. Applying the compression-based Ziv-Merhav estimator of
irreversibility to representations, we recover irreversibility trends across
complex Ginzburg-Landau patterns varying widely in spatiotemporal frequency and
noise level. Irreversibility estimates from representations similarly
recapitulate cell-activity trends in a Rho-GTPase patterning system undergoing
metabolic inhibition. Additionally, we find that our irreversibility estimates
serve as a dynamical order parameter, distinguishing stable and chaotic
dynamics in these nonlinear systems. Our framework leverages advances in deep
learning to offer robust, model-free measurements of nonequilibrium and
nonlinear behavior in complex living processes.
