161 citations · 288 across the 26 of their papers we have counts for
28 papers
Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method
George Chumbipuma, Irina Tezaur, Alejandro Diaz +1
We develop a hybrid modeling framework for coupling pre-trained numerics-informed neural networks (NINNs) with classical full order models (FOMs) using the overlapping Schwarz alte…
A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system
Chen Liu, Beatrice Riviere, Jie Shen +1
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a post processing procedure of solving a constrained mi…
FMG-Net and W-Net: Multigrid Inspired Deep Learning Architectures For Medical Imaging Segmentation
Adrian Celaya, Beatrice Riviere, David Fuentes
Accurate medical imaging segmentation is critical for precise and effective medical interventions. However, despite the success of convolutional neural networks (CNNs) in medical i…
Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem
Keegan L. A. Kirk, Rami Masi, Beatrice Riviere
The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the num…
A Generalized Surface Loss for Reducing the Hausdorff Distance in Medical Imaging Segmentation
Adrian Celaya, Beatrice Riviere, David Fuentes
Within medical imaging segmentation, the Dice coefficient and Hausdorff-based metrics are standard measures of success for deep learning models. However, modern loss functions for…
Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System
Chen Liu, Rami Masri, Beatrice Riviere
This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algorithm for solving the Cahn-Hilliard-Navier-Stokes equations within a decoupled splitting framew…