Neural optimization recovers Gaussian extremizers for Schrödinger Strichartz inequalities and shows mKdV breathers approaching the Frank-Sabin bound from below for the critical Airy-Strichartz inequality.
Alejo, Lucrezia Cossetti, Luca Fanelli, Claudio Muñoz, and Nicolás Valenzuela
2 Pith papers cite this work. Polarity classification is still indexing.
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Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.
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Neural Discovery of Strichartz Extremizers
Neural optimization recovers Gaussian extremizers for Schrödinger Strichartz inequalities and shows mKdV breathers approaching the Frank-Sabin bound from below for the critical Airy-Strichartz inequality.
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Random Neural Network Expressivity for Non-Linear Partial Differential Equations
Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.