4 papers
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…
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Claudio Muñoz, Nicolás Valenzuela
We present a comprehensive framework for deriving rigorous and efficient bounds on the approximation error of deep neural networks in PDE models characterized by branching mechanis…