Error-Correcting Neural Networks for Semi-Lagrangian Advection in the Level-Set Method

  title={Error-Correcting Neural Networks for Semi-Lagrangian Advection in the Level-Set Method},
  author={Luis {\'A}ngel Larios-C{\'a}rdenas and Fr{\'e}d{\'e}ric Gibou},
  journal={J. Comput. Phys.},

Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-set Method

An error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method and introduces dimensionless parametrization and probabilistic subsampling during data production to improve the accuracy and efficiency of curvature calculations around under-resolved regions.

Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method

This work develops a single pair of neural models in R 3 that can yield more accurate mean-curvature estimations in the L 1 and L ∞ norms than modern particle-based interface reconstruction and level-set schemes around under-resolved regions.



Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations

This work introduces a machine learning technique based on a deep neural network architecture that corrects the numerical errors induced by a coarse-grid simulation of turbulent flows at high-Reynolds numbers, while simultaneously recovering an estimate of the high-resolution fields.

Neural Networks and Deep Learning: A Textbook

The neural networks and deep learning a textbook is universally compatible in the manner of any devices to read in the digital library.

Parallel level-set methods on adaptive tree-based grids

A second order accurate level set method on non-graded adaptive cartesian grids

Tree Methods for Moving Interfaces

The methods combine a level set approach with frequent redistancing and semi-Lagrangian time stepping schemes which are explicit yet unconditionally stable to solve moving interface problems involving merging, anisotropy, faceting, and curvature.

TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems

  • 2015

OpenBLAS: An optimized BLAS library

  • OpenBLAS, July
  • 2021

A hybrid inference system for improved curvature estimation in the level-set method using machine learning