10 citations · 11 across the 4 of their papers we have counts for
3 papers · 1 filter
PDE Models for Deep Neural Networks: Learning Theory, Calculus of Variations and Optimal Control
Peter Markowich, Simone Portaro
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both net…
Self-regulated biological transportation structures with general entropy dissipation: 2D case and leaf-shaped domain
Clarissa Astuto, Peter Markowich, Simone Portaro +1
In recent years, the study of biological transportation networks has attracted significant interest, focusing on their self-regulating, demand-driven nature. This paper examines a…
Measure-based approach to mesoscopic modeling of optimal transportation networks
Jan Haskovec, Peter Markowich, Simone Portaro
We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the…