23 citations · 106 across the 22 of their papers we have counts for
4 papers · 1 filter
Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics
José A. Carrillo, Bertram Düring, Lisa Maria Kreusser +1
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotr…
Detection of high codimensional bifurcations in variational PDEs
Lisa Maria Kreusser, Robert I McLachlan, Christian Offen
We derive bifurcation test equations for A-series singularities of nonlinear functionals and, based on these equations, we propose a numerical method for detecting high codimension…
A Deterministic Gradient-Based Approach to Avoid Saddle Points
Lisa Maria Kreusser, Stanley J. Osher, Bao Wang
Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models efficiently. First-order methods such as gradient des…
Auxin transport model for leaf venation
Jan Haskovec, Henrik Jönsson, Lisa Maria Kreusser +1
The plant hormone auxin controls many aspects of the development of plants. One striking dynamical feature is the self-organisation of leaf venation patterns which is driven by hig…