1 citations · 1 across the 5 of their papers we have counts for
7 papers
Auxiliary Gradient-Flow Solvers for Generalized Newtonian Models
Stefano Zampini, Daniele Boffi, Gurt Dovletov +1
We introduce an auxiliary gradient-flow framework for variational problems with generalized Newtonian structure governed by an N-function. The key idea is to replace the nonlinear…
Gradient Flows for the -Laplacian Arising from Biological Network Models: A Novel Dynamical Relaxation Approach
Jan Haskovec, Peter Markowich, Stefano Zampini
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral…
Robust and scalable nonlinear solvers for finite element discretizations of biological transportation networks
Jan Haskovec, Peter Markowich, Simone Portaro +1
We develop robust and scalable fully implicit nonlinear finite element solvers for the simulations of biological transportation networks driven by the gradient flow minimization of…
Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations
Nuno J. Alves, Peter Markowich, Athanasios E. Tzavaras
We study a one-dimensional nonlinear Vlasov equation with a local self-consistent force field generated by the density, where the force is given by the spatial derivative of a real…
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…