  We introduce an adaptive refinement procedure for smart, and scalable
abstraction of dynamical systems. Our technique relies on partitioning the
state space depending on the observation of future outputs. However, this
knowledge is dynamically constructed in an adaptive, asymmetric way. In order
to learn the optimal structure, we define a Kantorovich-inspired metric between
Markov chains, and we use it as a loss function. Our technique is prone to
data-driven frameworks, but not restricted to.
  We also study properties of the above mentioned metric between Markov chains,
which we believe could be of application for wider purpose. We propose an
algorithm to approximate it, and we show that our method yields a much better
computational complexity than using classical linear programming techniques.
