“A biologically inspired deduction of Optimal Transport Problems” – Enrico Facca (Scuola Normale Superiore)

Abstract

We present a model originally inspired by the study of a unicellular slime mold (called Physarum Polycephalum). The model couples a diffusion equation with an ODE imposing a transient dynamics postulating that the diffusion coefficient grows with the magnitude of the transport flux counterbalanced by a linear decay. We conjecture that this system converges toward the solution of the Monge-Kantorovich Equations, a PDE-based formulation of L1-Optimal Transport Problem. Moreover, when a non-linearity is introduced into the dynamic equation for the diffusion coefficient, the equilibrium configurations of the system are reminiscent of solutions of the Congested and the Branched Transport Problems, finding applications in the study of natural transport networks. We present theoretical and numerical evidences corroborating our conjectures, together with some open questions. The seminar will be performed online and will be available at the website https://meet.google.com/pvy-cjzz-iky

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