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math.NA2024★ 11 cited
Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
Joubine Aghili, Emmanuel Franck, Romain Hild +2
It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to…
math.NA2024
A Dynamical Neural Galerkin Scheme for Filtering Problems
Joubine Aghili, Joy Zialesi Atokple, Marie Billaud-Friess +3
This paper considers the filtering problem which consists in reconstructing the state of a dynamical system with partial observations coming from sensor measurements, and the knowl…