Beatrice Riviere

About

Beatrice Riviere is a chaired professor at the Department of Computational Applied Mathematics and Operations Research at Rice University. She serves as the principal investigator (PI) of the COMP-M consortium, which focuses on computational modeling of porous media. Her role involves leading research efforts within the COMP-M team, which comprises faculty, postdoctoral fellows, and graduate students dedicated to advancing the understanding and simulation of porous media phenomena.

Research topics

• Machine Learning
• Artificial Intelligence
• Computer Science
• Mathematics
• Applied mathematics
• Mathematical analysis
• Mechanics
• Physics

Selected publications

• PocketNet: A Smaller Neural Network for Medical Image Analysis

  IEEE Transactions on Medical Imaging · 2022 · 37 citations

  Medical imaging deep learning models are often large and complex, requiring specialized hardware to train and evaluate these models. To address such issues, we propose the PocketNet paradigm to reduce the size of deep learning models by throttling the growth of the number of channels in convolutional neural networks. We demonstrate that, for a range of segmentation and classification tasks, PocketNet architectures produce results comparable to that of conventional neural networks while reducing…

  DOI

• A discontinuous Galerkin pressure correction scheme for the incompressible Navier–Stokes equations: Stability and convergence

  Mathematics of Computation · 2022 · 30 citations

  Senior authorCorresponding

  A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier–Stokes equations is formulated and analyzed. We prove unconditional stability of the proposed scheme. Convergence of the discrete velocity is established by deriving a priori error estimates. Numerical results verify the convergence rates.

  DOI

• Convergence of a Decoupled Splitting Scheme for the Cahn–Hilliard–Navier–Stokes System

  SIAM Journal on Numerical Analysis · 2023-11-15 · 20 citations

  articleSenior author

  .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 framework. We show that the proposed scheme is uniquely solvable and mass conservative. The energy dissipation and the \(L^\infty\) stability of the order parameter are obtained under a CFL-like constraint. Optimal a priori error estimates in the broken gradient norm and in the \(L^2\) norm are derived. The stability proofs…

  PublisherDOI

• A Simple and Efficient Convex Optimization Based Bound-Preserving High Order Accurate Limiter for Cahn–Hilliard–Navier–Stokes System

  SIAM Journal on Scientific Computing · 2024-06-03 · 16 citations

  article
  PublisherDOI

• Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

  International Journal for Numerical Methods in Engineering · 2023-11-12 · 5 citations

  articleSenior authorCorresponding

  Abstract This paper presents a numerical study of immiscible, compressible two‐phase flows in porous media, that takes into account heterogeneity, gravity, anisotropy and injection/production wells. We formulate a fully implicit stable discontinuous Galerkin solver for this system that is accurate, that respects maximum principle for the approximation of saturation, and that is locally mass conservative. To completely eliminate the overshoot and undershoot phenomena, we construct a flux limiter…

  PublisherDOI

Recent grants

• High order numerical methods for multiphysics couplings

  NSF · $342k · 2008–2013

• Collaborative Research: Mathematical Modeling of Biological Processes in Edematous Tissue

  NSF · $228k · 2013–2017

• Coupling Complex Flow and Transport Phenomena

  NSF · $150k · 2005–2008

Frequent coauthors

• David Fuentes

  42 shared

• Vivette Girault

  Laboratoire Jacques-Louis Lions

  38 shared

• Adrian Celaya

  The University of Texas MD Anderson Cancer Center

  35 shared

• Jonas Actor

  31 shared

• Caroline Chung

  The University of Texas MD Anderson Cancer Center

  28 shared

• Evan Gates

  The University of Texas MD Anderson Cancer Center

  28 shared

• Dawid Schellingerhout

  Eulji University Hospital

  27 shared

• M. Rajarajeswari

  The University of Texas MD Anderson Cancer Center

  27 shared

Labs

• Visiting & Postdoctoral ResearchersPI

Education

• Ph.D., Oden Institute

  University of Texas at Austin

  2000

• Master, Mathematics

  Pennsylvania State University

  1996

• Diplome d' ingenieur

  École Centrale de Lyon

  1995

Awards & honors

• AWM Fellow (2022)
• SIAM Fellow (2021)
• Elected President SIAM TX-LA Section (2020-2022)
• Elected Chair SIAM Activity Group on Geosciences (2019-2020)

Similar researchers at Rice University

• Shiqian Mah-38
• Andrew J. Schaeferh-36
• Matthias Heinkenschlossh-34