  For real-world complex system constantly enduring perturbation, to achieve
survival goal in changing yet unknown environments, the central problem is
designing a self-adaptation strategy instead of fixed control strategies, which
enables system to adjust its internal multi-scale structure according to
environmental feedback. Inspired by thermodynamics, we develop a self-adaptive
network utilizing only macroscopic information to achieve desired landscape
through reconfiguring itself in unknown environments. By continuously
estimating environment entropy, our designed self-adaptive network can
adaptively realize desired landscape represented by topological measures. The
adaptability of this network is achieved under several scenarios, including
confinement on phase space and geographic constraint. The adaptation process is
described by relative entropy corresponding to the Boltzmann H function, which
decreases with time following unique power law distinguishing our self-adaptive
network from memoryless systems. Moreover, we demonstrate the transformability
of our self-adaptive network, as a critical mechanism of complex system
resilience, allowing for transitions from one target landscape to another.
Compared to data-driven methods, our self-adaptive network is understandable
without careful choice of learning architecture and parameters. Our designed
self-adaptive network could help to understand system intelligence through the
lens of thermodynamics.
