167 citations · 1.3k across the 78 of their papers we have counts for
7 papers · 1 filter
On the approximation of rough functions with deep neural networks
Tim De Ryck, Siddhartha Mishra, Deep Ray
Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast…
Statistical solutions of the incompressible Euler equations
Samuel Lanthaler, Siddhartha Mishra, Carlos Parés-Pulido
We propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are time-parameterized probability measures on…
A Multi-level procedure for enhancing accuracy of machine learning algorithms
Kjetil O. Lye, Siddhartha Mishra, Roberto Molinaro
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in syst…
Statistical solutions of hyperbolic systems of conservation laws: numerical approximation
Ulrik Skre Fjordholm, Kjetil Lye, Siddhartha Mishra +1
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncert…
Arbitrarily high-order (weighted) essentially non-oscillatory finite difference schemes for anelastic flows on staggered meshes
Siddhartha Mishra, Carlos Parés-Pulido, Kyle G. Pressel
We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids…
On the convergence of the spectral viscosity method for the two-dimensional incompressible Euler equations with rough initial data
Samuel Lanthaler, Siddhartha Mishra
We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large…