Publications by Deep Ray | EPFL Graph Search

Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows

A projection-based reduced order model (ROM) based on the Fourier collocation method is proposed for compressible flows. The incorporation of localized artificial viscosity model and filtering is pursued to enhance the robustness and accuracy of the ROM fo ...

GLOBAL SCIENCE PRESS2022

Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks

Jan Sickmann Hesthaven, Deep Ray, Lukas Schwander

While a nonlinear viscosity is used widely to control oscillations when solving conservation laws using high-order elements based methods, such techniques are less straightforward to apply in global spectral methods since a local estimate of the solution r ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Jan Sickmann Hesthaven, Niccolo' Discacciati, Deep Ray

High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amoun ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

An artificial neural network as a troubled-cell indicator

Jan Sickmann Hesthaven, Deep Ray

High-resolution schemes for conservation laws need to suitably limit the numerical solution near discontinuities, in order to avoid Gibbs oscillations. The solution quality and the computational cost of such schemes strongly depend on their ability to corr ...

2018

Detecting troubled-cells on two-dimensional unstructured grids using a neural network

Jan Sickmann Hesthaven, Deep Ray

In a recent paper [Ray and Hesthaven, J. Comput. Phys. 367 (2018), pp 166-191], we proposed a new type of troubled-cell indicator to detect discontinuities in the numerical solutions of one-dimensional conservation laws. This was achieved by suitably train ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2018

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

Qian Wang, Jan Sickmann Hesthaven, Deep Ray

A non-intrusive reduced-basis (RB) method is proposed for parametrized unsteady flows. A set of reduced basis functions are extracted from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD), and the coefficients of the redu ...

2018