# Research

## Motivation

The goal of my research is to develop mathematical models and scalable algorithms to understand large-scale physical systems. I strongly believe in the importance of theoretical methods that are grounded in real-world problems, and that a profound understanding of foundational aspects of mathematics is a consequence of experimental observations.

## Current research

I study routing problems on networks combining techniques stemming from optimal transport and statistical physics. In particular, I am interested in explaining how different route selection mechanisms affect traffic on networks. The applications of my work span from urban and biological networks, to machine learning.

**Technical details:** the approach we are using to solve network routing problems is to map them to an equivalent minimal-flow formulation, allowing to study the effect of interacting agents which are competing on (possibly composite) shared infrastructures. Solutions of such models can be found searching for stationary trajectories of an optimal transport based dynamical system, regulating edge capacities and fluxes on the network [1, 2]. One remarkable advantage of our method is that convergence can be rapidly achieved using efficient solvers, since the problem formulation can be further reduced to the iterative solution of a linear system of equations [1]. Moreover, our models bear a close relationship with optimal transport in continuous domains, for which the equivalent counterpart of our algorithm has been used as a tool for network extraction from continuous distributions [3, 4].

Network formation in Physarum polycephalum [5], archetype of self-organizing system from which our methods are largely inspired.

## References

[1] *A. Lonardi, E. Facca, M. Putti, and C. De Bacco, Designing optimal networks for multicommodity transport problem, 2021.*

[2] *A. Lonardi, M. Putti, and C. De Bacco, Multicommodity routing optimization for engineering networks, 2021.*

[3] *D. Baptista, D. Leite, E. Facca, M. Putti, and C. De Bacco, Network extraction by routing optimization, 2020.*

[4] *D. Baptista and C. De Bacco, Principled network extraction from images, 2021*.

[5] *A. Tero, et al., Rules for Biologically Inspired Adaptive Network Design, 2010*.