167 citations · 1.3k across the 78 of their papers we have counts for
7 papers · 2 filters
A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer
Gioele Janett, Oskar Steiner, Ernest Alsina Ballester +2
Context. Several numerical problems require the interpolation of discrete data that present various types of discontinuities. The radiative transfer is a typical example of such a…
Well-posedness of Bayesian inverse problems for hyperbolic conservation laws
Siddhartha Mishra, David Ochsner, Adrian M. Ruf +1
We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (po…
On universal approximation and error bounds for Fourier Neural Operators
Nikola Kovachki, Samuel Lanthaler, Siddhartha Mishra
Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are un…
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs
Tim De Ryck, Siddhartha Mishra
Physics informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred by PINNs in approximating the sol…
On the approximation of functions by tanh neural networks
Tim De Ryck, Samuel Lanthaler, Siddhartha Mishra
We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic ta…
Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs
Genming Bai, Ujjwal Koley, Siddhartha Mishra +1
We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-…