  Reaction-diffusion systems have been proposed as a model for pattern
formation and morphogenesis. The Fickian diffusion typically employed in these
constructions model the Brownian motion of particles. The biological and
chemical elements that form the basis of this process, like cells and proteins,
occupy finite mass and volume and interact during migration. We propose a
Reaction-diffusion system with Maxwell-Stefan formulation to construct the
diffusive flux. This formulation relies on inter-species force balance and
provides a more realistic model for interacting elements. We also present a
variational system inference-based technique to extract these models from
spatiotemporal data for these processes. We show that the inferred models can
capture the characteristics of local Turing instability that instigates the
pattern formation process. Moreover, the equilibrium solutions of the inferred
models form similar patterns to the observed data.
