4 papers
Approximation of solutions of parameter-dependent problems by residual neural networks
Ana Carpio
We develop a convergent scheme to train neural networks involving analytic activation functions based on gradient flows. Convergence properties are guaranteed by Lojasiewicz theory…
Hierarchical topological clustering
Ana Carpio, Gema Duro
Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm t…
Asymptotic models for the evolution of a circular biofilm
Diego Alonso-Orán, Ana Carpio, Rafael Granero-Belinchón
We study a class of lubrication-type equations modeling the spread of thin poroelastic biofilms at air/agar interfaces. Starting from a biofilm slab model, we perform a formal mult…
Analysis of a two phase flow model of biofilm spread
Ana Carpio, Gema Duro
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemica…