A general error analysis for randomized low-rank approximation with application to data assimilation

no code implementations • 8 May 2024 • Alexandre Scotto Di Perrotolo, Youssef Diouane, Selime Gürol, Xavier Vasseur

However, despite the large variety of algorithms, the existing theoretical frameworks for their analysis rely on a specific structure for the covariance matrix that is not adapted to all the algorithms.

On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method

no code implementations • 9 Apr 2019 • Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur

Here a feedforward neural network is used to approximate the solution of the partial differential equation.