Dresden 2026 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 4: Poster Session
SOE 4.5: Poster
Monday, March 9, 2026, 18:00–21:00, P4
Optimal transport with constraints: from mirror descent to classical mechanics — •Abdullahi Ibrahim1,2, Michael Muehlebach2, Caterina De Bacco2, and Dirk Brockmann1 — 1Center Synergy of Systems, Dresden University of Technology, Dresden, Germany — 2Max Planck Institute for Intelligent Systems, Cyber Valley, Tuebingen 72076, Germany
Over the past decades, a variety of transportation systems have been successfully modelled using optimal transport (OT), from biological networks as leaf venation, to engineering networks as urban transportation. In this context, adaptation equations that describe how conductivities, flows and pressure potentials evolve interdependently to consolidate into an optimal network structure. This has been used extensively to study a variety of transportation scenarios, and it has been shown to explain with a high degree of similarity observed on real networks. However, current approaches based on adaptation equations suffer from not considering constraints (beyond standard ones like conservation of mass and positivity) as part of the general framework. As a result, networks output from these models can be unrealistic in practice. We address this flaw by proposing a general framework powerful enough to accommodate nonlinear and nonconvex constraints in OT problems. Our approach follows a physics-based perspective on including constraints by leveraging the principle of d'Alembert-Lagrange from classical mechanics. This leads to a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates.
Keywords: Network flow optimization; dynamics of transport network; traffic dynamics; optimal transport