4 papers · 1 filter
Neural Discovery of Strichartz Extremizers
Nicolás Valenzuela, Ricardo Freire, Claudio Muñoz
Strichartz inequalities are a cornerstone of the modern theory of dispersive PDEs, but their extremizers are known explicitly only in a handful of sharp cases. The non-convexity of…
Error bounds for Physics Informed Neural Networks in Generalized KdV Equations placed on unbounded domains
Ricardo Freire, Claudio Muñoz, Nicolás Valenzuela
In this paper we study a rigorous setting for the numerical approximation via deep neural networks of the generalized Korteweg-de Vries (gKdV) model in one dimension, for subcritic…
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Miguel Á. Alejo, Lucrezia Cossetti, Luca Fanelli +2
We consider the subcritical nonlinear Schrödinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximat…
A numerical approach for the fractional Laplacian via deep neural networks
Nicolás Valenzuela
We consider the fractional elliptic problem with Dirichlet boundary conditions on a bounded and convex domain of , with . In this paper, we perform a st…