Irene Fonseca

About

Irene Fonseca is the Kavčić-Moura University Professor of Mathematics and the Director of the Center for Nonlinear Analysis at Carnegie Mellon University. Her primary focus is on research and training in applied mathematics at the broad interface between mathematics, the physical sciences, and engineering. Her research program includes the mathematical study of shape memory alloys, ferroelectric and magnetic materials, composites, thin structures, phase transitions in fluids and solids, and the mathematical analysis of image segmentation, denoising, detexturing, and recolorization in computer vision. She has received numerous awards, including the International Society for the Interaction of Mechanics and Mathematics Senior Prize, and is a Fellow of the European Academy of Sciences, the American Mathematical Society, and SIAM. She has also served as the Past President of SIAM.

Research topics

• Artificial Intelligence
• Data Mining
• Computer Science
• Algorithm
• Applied mathematics
• Mathematics
• Mathematical analysis
• Mathematical optimization

Selected publications

• Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme

  Journal of Nonlinear Science · 2023 · 8 citations

  -convergence under a conditional uniform bound on the trace constant of the operators and a finite-null-space condition. Some first examples and numerical results are given.

  PublisherOA PDFDOI

• Homogenization and Phase Separation with Space Dependent Wells: The Subcritical Case

  Archive for Rational Mechanics and Analysis · 2023-08-29 · 6 citations

  articleOpen access

  Abstract A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are allowed to move and to have discontinuities. The zeroth and first order $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Γ</mml:mi></mml:math> -limits are identified. The topology considered for the latter is that of two-sca…

  PublisherOA PDFDOI

• Dyadic Partition-Based Training Schemes for TV/TGV Denoising

  Journal of Mathematical Imaging and Vision · 2024-10-23 · 4 citations

  articleOpen access

  Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best-known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these automatically through multilevel approaches, for example by optimizing performance on noisy/clean image pairs. In…

  PublisherOA PDFDOI

• Global and local energy minimizers for a nanowire growth model

  Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2022-11-04 · 4 citations

  articleOpen access1st authorCorresponding

  We consider a model for vapor–liquid–solid growth of nanowires proposed in the physical literature. Liquid drops are described as local or global volume-constrained minimizers of the capillarity energy outside a semi-infinite convex obstacle modeling the nanowire. We first address the existence of global minimizers and then, in the case of rotationally symmetric nanowires, we investigate how the presence of a sharp edge affects the shape of local minimizers and the validity of Young’s law.

  PublisherDOI

• The mathematics of thin structures

  Quarterly of Applied Mathematics · 2022-09-01 · 3 citations

  articleOpen access

  This article offers various mathematical contributions to the behavior of thin films. The common thread is to view thin film behavior as the variational limit of a three-dimensional domain with a related behavior when the thickness of that domain vanishes. After a short review in Section 1 of the various regimes that can arise when such an asymptotic process is performed in the classical elastic case, giving rise to various well-known models in plate theory (membrane, bending, Von Karmann, etc…)…

  PublisherOA PDFDOI

Recent grants

• Variationals Methods in Imaging and in Materials

  NSF · $1.2M · 2009–2015

• Center for Nonlinear Analysis: Research and Training in Applied Mathematics

  NSF · $745k · 2004–2009

• Variational Methods for Materials and Imaging Sciences

  NSF · $1.2M · 2014–2020

Frequent coauthors

• Giovanni Leoni

  60 shared

• Gilles A. Francfort

  Flatiron Health (United States)

  27 shared

• Andrea Braides

  18 shared

• Paolo Marcellini

  16 shared

• Elisa Davoli

  TU Wien

  15 shared

• Nicola Fusco

  University of Naples Federico II

  14 shared

• Massimiliano Morini

  13 shared

• Gianni Dal Maso

  13 shared

Labs

• Irene FonsecaPI

Education

• Ph.D., Minneapolis

  University of Minnesota

Awards & honors

• Senior Prize Fellow of the European Academy of Sciences
• Fellow of the American Mathematical Society
• SIAM Fellow

Similar researchers at Carnegie Mellon University

• Alan Friezeh-74
• Michael Youngh-57
• David Kinderlehrerh-45