42 citations · 57 across the 10 of their papers we have counts for
15 papers
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…
Nonlocal vector calculus on the sphere
Hadrien Montanelli, Richard Mikael Slevinsky, Qiang Du
We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar…
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…
The linear sampling method for random sources
Josselin Garnier, Houssem Haddar, Hadrien Montanelli
We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justif…
Computing weakly singular and near-singular integrals over curved boundary elements
Hadrien Montanelli, Matthieu Aussal, Houssem Haddar
We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the…
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…
A spectral method for nonlocal diffusion operators on the sphere
Richard Mikael Slevinsky, Hadrien Montanelli, Qiang Du
We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlo…
New error bounds for deep networks using sparse grids
Hadrien Montanelli, Qiang Du
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks. We present new error estimates for which the curse of the dimensionality is lessene…
Fourth-order time-stepping for stiff PDEs on the sphere
Hadrien Montanelli, Yuji Nakatsukasa
We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the…
Computing hyperbolic choreographies
Hadrien Montanelli
An algorithm is presented for numerical computation of choreographies in spaces of constant negative curvature in a hyperbolic cotangent potential, extending the ideas given in a c…
Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators
Hadrien Montanelli, Niall Bootland
Dozens of exponential integration formulas have been proposed for the high-accuracy solution of stiff PDEs such as the Allen-Cahn, Korteweg-de Vries and Ginzburg-Landau equations.…
Extension of Chebfun to periodic functions
Grady B. Wright, Mohsin Javed, Hadrien Montanelli +1
Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, includin…
Computing planar and spherical choreographies
Hadrien Montanelli, Nikola Ivanov Gushterov
An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic…