167 citations · 1.3k across the 78 of their papers we have counts for
11 papers · 1 filter
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…
Long Expressive Memory for Sequence Modeling
T. Konstantin Rusch, Siddhartha Mishra, N. Benjamin Erichson +1
We propose a novel method called Long Expressive Memory (LEM) for learning long-term sequential dependencies. LEM is gradient-based, it can efficiently process sequential tasks wit…
On the vanishing viscosity limit of statistical solutions of the incompressible Navier-Stokes equations
Ulrik Skre Fjordholm, Siddhartha Mishra, Franziska Weber
We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures, which are pr…
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…