5 papers · 1 filter
A neural operator framework for solving inverse scattering problems
Victor Chenu, Houssem Haddar, Hadrien Montanelli
We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropri…
Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations
Luiz Maltez Faria, Pierre Marchand, Hadrien Montanelli
We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our…
The linear sampling method for data generated by small random scatterers
J. Garnier, H. Haddar, H. Montanelli
We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scat…
Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem
Hadrien Montanelli, Haizhao Yang
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a co…
Deep ReLU networks overcome the curse of dimensionality for bandlimited functions
Hadrien Montanelli, Haizhao Yang, Qiang Du
We prove a theorem concerning the approximation of bandlimited multivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome. Our theorem is ba…