3 papers
Tropical Geometry as a Restricted Architecture for Physics-Informed Neural Networks: Applications in Nonlinear Fluid-Structure Examples
Carla Valencia-Negrete, Cristhian Garay-Lopez, Marco Favela-Rodriguez +1
Nonlinear algebraic (polynomial) differential equations that govern fluid-structure interactions, such as those modeling vortex-induced vibrations, and shock waves, often lack anal…
Elementary solutions of ordinary tropical differential equations, and vanishing orders of solutions of algebraic differential equations
Cristhian Garay-López, Johana Luviano-Flores, Carla Valencia-Negrete
Our aim is to use tropical differential algebra to systematically build a combinatorial basis for the study of the set of (formal) power series solutions to nonlinear algebraic ord…
Tropical initial degeneration for systems of algebraic differential equations
Lara Bossinger, Sebastian Falkensteiner, Cristhian Garay-López +1
We study the notion of degeneration for affine schemes associated to systems of algebraic differential equations with coefficients in the fraction field of a multivariate formal po…