A neural network based shock detection and localization approach for discontinuous Galerkin methods
The stable and accurate approximation of discontinuities such as shocks on a finite
computational mesh is a challenging task. Detection of shocks or strong discontinuities in …
computational mesh is a challenging task. Detection of shocks or strong discontinuities in …
An unsupervised machine-learning-based shock sensor: Application to high-order supersonic flow solvers
We present a novel unsupervised machine-learning shock sensor based on Gaussian
Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in …
Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in …
Using Deep Neural Networks for Detecting Spurious Oscillations in Discontinuous Galerkin Solutions of Convection-Dominated Convection–Diffusion Equations
D Frerichs-Mihov, L Henning, V John - Journal of Scientific Computing, 2023 - Springer
Standard discontinuous Galerkin finite element solutions to convection-dominated
convection–diffusion equations usually possess sharp layers but also exhibit large spurious …
convection–diffusion equations usually possess sharp layers but also exhibit large spurious …
Neural network-based limiter with transfer learning
Recent works have shown that neural networks are promising parameter-free limiters for a
variety of numerical schemes (Morgan et al. in A machine learning approach for detecting …
variety of numerical schemes (Morgan et al. in A machine learning approach for detecting …
A priori neural networks versus a posteriori mood loop: a high accurate 1d fv scheme testing bed
A Bourriaud, R Loubère, R Turpault - Journal of Scientific Computing, 2020 - Springer
In this work we present an attempt to replace an a posteriori MOOD loop used in a high
accurate Finite Volume (FV) scheme by a trained artificial Neural Network (NN). The MOOD …
accurate Finite Volume (FV) scheme by a trained artificial Neural Network (NN). The MOOD …
Machine learning approaches for the solution of the riemann problem in fluid dynamics: a case study
We present our results by using a machine learning (ML) approach for the solution of the
Riemann problem for the Euler equations of fluid dynamics. The Riemann problem is an …
Riemann problem for the Euler equations of fluid dynamics. The Riemann problem is an …
Artificial neural network-augmented stabilized finite element method
An artificial neural network-augmented Streamline Upwind/Petrov-Galerkin finite element
scheme (SPDE-NetII) is proposed for solving singularly perturbed partial differential …
scheme (SPDE-NetII) is proposed for solving singularly perturbed partial differential …
AI-augmented stabilized finite element method
An artificial intelligence-augmented Streamline Upwind/Petrov-Galerkin finite element
scheme (AiStab-FEM) is proposed for solving singularly perturbed partial differential …
scheme (AiStab-FEM) is proposed for solving singularly perturbed partial differential …
On the choice of hyper-parameters of artificial neural networks for stabilized finite element schemes
This paper provides guidelines for an effective artificial neural networks (ANNs) design to
aid stabilized finite element schemes. In particular, ANNs are used to estimate the …
aid stabilized finite element schemes. In particular, ANNs are used to estimate the …
On slope limiting and deep learning techniques for the numerical solution to convection-dominated convection-diffusion problems
D Frerichs-Mihov - 2023 - refubium.fu-berlin.de
As the first main topic, several slope-limiting techniques from the literature are presented,
and various novel methods are proposed. These post-processing techniques aim to …
and various novel methods are proposed. These post-processing techniques aim to …