Scientific Computing @ Emory on Emory Scientific Computing Group

People

Fri, 13 Jul 2018 10:35:08 -0400

Faculty

Julianne Chung	Matthias Chung	Bree Ettinger	Manuela Girotti
Manuela Manetta	Talea Mayo	James Nagy	Elizabeth Newman
Levon Nurbekyan	Lars Ruthotto	Marco Tezzele	Alessandro Veneziani
Yuanzhe Xi

IRtools: MATLAB Package for Large Scale Inverse Problems

Sat, 23 Sep 2017 09:59:16 -0400

The aim of this project is to develop a new MATLAB software package that consists of state-of-the-art iterative methods to solve large scale ill-posed inverse problems. The package allows users to easily experiment with different iterative methods (including several new approaches) and regularization strategies with very little programming effort. The package also includes several test problems and examples to illustrate how the iterative methods can be used on a variety of large-scale inverse problems.

A Flexible Optimal Control Framework for Efficient Training of Deep Neural Networks

Mon, 30 Jan 2017 09:59:16 -0400

This project develops a new mathematical framework for deep learning based on the interpretation of certain deep neural networks as nonlinear time-dependent differential equations. This interpretation offers a new way to analyze the successes and failures of deep learning. Advances in deep learning will be made by adapting the wide array of tools available for related optimal control problems, including numerical optimization, partial and ordinary differential equations, inverse problems theory, and parallel processing, to the deep learning problem. Using these currently untapped resources provides rigorous new ways to design and train very deep neural networks that generalize well.

People

Fri, 13 Jul 2018 10:35:08 -0400

Postdocs

John Darges NSF RTG	Chelsea Drum NSF RTG	Mikhail Lepilov NSF RTG	Lucas Onisk
Jimena Martin Tempestti	Tianshi Xu	Nicole Yang

LifeV - finite element 3D advanced C++ OO library

Thu, 08 Mar 2018 09:59:16 -0400

LifeV (to be read Life Five) is an open source library for the numerical solution of partial differential equations with the Finite Element Method (FEM). The choice of the FEM is motivated by its rigorous mathematical background, with a sound control of the accuracy, coupled with excellent flexibility in managing complex geometries. There are also LifeV modules for VTK and CGAL.

PI: Alessandro Veneziani

Novel methods for computational hemodynamics

Tue, 21 Nov 2017 09:59:16 -0400

The incompressible Navier-Stokes equations are the basic mathematical model for the simulation of blood flow in arteries. Even if well-known and investigated since a long time, these equations still represent a numerical challenge for their saddle-point structure, the non linear nature. In medical applications, efficiency is a priority together with reliability. All these aspects require the set up of appropriate preconditioners, specific solution methods and, more in general, approaches that could take advantage from particular features of the problem at hand. In addition, we should consider (i) the presence of possible turbulent dynamics and their appropriate numerical modeling; (ii) the lack of data that systematically affects the clinical scenarios (defective problems, image legacy problem). The former is currently solved by Large Eddie Simulation (LES) approaches, specifically based on deconvolution filters. The latter calls for specific methods for the identification of the (arbitrary) missing conditions with low impact on the final solutions. Also, the presence of numerical instabilities induced by backflows is a critical issues in computational hemodynamics. Among the possible solution methods, we also include the Hierarchical Model Reduction technique, a numerical approach for incompressible flow in pipes, where finite elements or isogeometric analysis for the axial direction of the pipe are coupled with spectral methods for a rapid simulation of the transversal dynamics.

People

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Graduate Students

Quincy Alston	Francesco Brarda	Ariana Brown	Elle Buser
Yizhou (Riley) Chen	Alex Dunbar	Emma Hart	Katherine Keegan
Leonardo Molinari	Imran Shah	Jack Michael Solomon	Mitchell Scott
Joseph Woods	Jiaqi Yang	Benjamin Yellin	Shifan Zhao

jInv - Julia Package for Parallel PDE Parameter Estimation

Fri, 22 Sep 2017 09:59:16 -0400

jInv is a flexible framework for PDE parameter estimation written in Julia. It gives easy access to many commonly used misfit and regularization terms, efficient numerical optimization, and a parallel and distributed computing model. We also have some examples online.

PI: Lars Ruthotto

Collaborators: Eldad Haber (UBC), Eran Treister (Ben Gurion University of the Negev, Israel), Patrick Belliveau, Dave Marchant, Christoph Schwarzbach

Efficient Algorithms for PDE-Parameter Estimation

Tue, 12 Sep 2017 09:59:16 -0400

This project develops efficient numerical methods for solving big data parameter estimation problems that involve partial differential equations (PDEs). Parameter estimation problems of this kind impose key challenges in many scientific disciplines, e.g., in medical imaging, geophysical imaging, and deep learning. The inverse problem can be formulated as an optimization problem with constraints that are given by the PDEs. The unknowns are parameters of the PDEs (e.g., physical properties of the object to be measured). The objective is to minimize the misfit between PDE simulations and measured data plus some regularization term.

People

Fri, 13 Jul 2018 10:35:08 -0400

Undergraduate Students

Kai Chang
Kristina Gong
Zoe Ji
Oliver Wang

FAIR - Flexible Algorithms for Image Registration

Fri, 22 Sep 2017 09:59:16 -0400

FAIR is written in Matlab and provides implementations of most state-of-the-art image registration algorithms. Although it is primarily designed as an academic and teaching tool, it offers great potential for developing prototypes and solving real-life problems.

PI: Lars Ruthotto

Collaborators: Jan Modersitzki (Fraunhofer MEVIS and University of Luebeck, Germany) and Andreas Mang (University of Houston)

Algorithms for Inverse Problems that Exploit Kronecker Product and Tensor Structures

Mon, 11 Sep 2017 09:59:16 -0400

The aim of this project is to develop efficient singular value decomposition (SVD) approximation methods for large-scale matrices that arise in discrete ill-posed inverse problems. The approach will exploit inherent Kronecker product and tensor structures, and will be the basis for a computational platform for the efficient solution of large-scale ill-posed problems. Efficient approaches to solve Kronecker product and tensor structured SVD updating problems will be developed. Iterative methods that can incorporate regularization, sparse and low-rank constraints on the solution will also be considered. The SVD approximations and updating methods developed in this project can be used as tools to obtain approximate solutions of ill-posed inverse problems, as preconditioners to accelerate iterative solvers, or as tools to build solution methods for nonlinear problems. By developing a computational platform, based on SVD approximations, the work developed in this proposal will have a broad scientific impact for applications where it is necessary to compute solutions of large-scale ill-posed inverse problems, including astronomy, cosmology, geophysics, microscopy, and medical imaging.

People

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Alumni

People

Fri, 13 Jul 2018 10:35:08 -0400

Former Honors Students

Zhiqi Fu, BS 2020
Mengtong Hu, BS 2019
Derek Zhang, BS 2019
Francis Yin, BS 2019
Sherry Huang, BS 2019
Tianhui Mao, BS 2019
Evan Scope Crafts, BS 2019
Kathy Wu, BS 2019
Derek Zhang, BS 2019
Wenda Zheng, BS 2018
Huiying Zhu, BS 2017
Siqi Xuo, BS 2017
Quiny She, BS 2017
Shuan Gao, BS 2017
Yiwen Guo, BS 2017
Raul Platero, BS 2017
Hanyong Wu, BS 2017
Huiying Zhu, BS 2017
Claire Lin, BS 2016
Lu Lin, BS 2016
Chang Meng, BS 2016
Sid Raju, BS 2016
Tianli Han, BS 2015
Hanqiu Xia, BS 2015
Brian Breeden, BS 2014
Shannon Buckley, BS 2014
Ngoc Hoang Lam Phan, BS 2014
Kexin Qu, BS 2014
Yuan Ye, BS 2014
Chen (Cool) Cheng, BS 2013
Warrick Macmillan, BS 2013
Yifan Wang, BS 2013
Josh Keller, BS 2011
James Nance, BS 2011
Ruth Blum, BS 2010
James Herring, BS 2010
Melissa Goldstein, BS 2006
Julianne Chung, BA 2004
Mili Shah, BS/MS 2002
Ryan Wright, BS/MS 2002
Sharriah Sulaiman, BS/MS 2001

People

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Former Postdocs

Difei Cang (2019-2023)
Malena Sabate Landman (2023-2024)
Deepanshu Verma (2021-2024)
Bas Peters (2020-2021)
Boyi Yang (2015-2017)
Gaetano Esposito (2014-2015)
Leandro Gryngarten (2013-2014)
Lina Merchan (2013-2014)
Tiziano Passerini (2009-2013)
Paola Boito (2009-2010)
Matthias Chung (2008-2010)
Luca Gerardo-Giorda (2008-2010)
Lucia Mirabella (2008-2010)
Mauro Perego (2008-2010)
Lior Horesh (2007–2009)
Stefan Heldmann (2006–2008)
Bora Ucar (2005–2006)

Former Graduate Students

Abbey Julian, PhD 2024
Xingjian Li, PhD 2024
Malvern Madondo, PhD 2024
Derek Onken, PhD 2021
Huijuan Xu, PhD 2020
Alessandro Barone, PhD 2019
Samy Wu Fung, PhD 2019
Sofia Guzzetti, PhD 2019
Blair Rossetti, PhD 2019
Yunyi Hu, PhD 2019
Clarissa Garvey, PhD 2018
Alex Viguerie, PhD 2018
Massimiliano Lupo Pasini, PhD 2018
James Lincoln Herring, PhD 2018
Isabel Chen, PhD 2016
Huanhuan Yang, PhD 2015
Boyi Yang, PhD 2015
Sebastian Berisha, PhD 2014
Luca Bertagna, PhD 2014
Qing Chu, PhD 2014
Anastasia Svischeva, PhD 2014
Christine Klymko, PhD 2014
Alexis Aposporidis, PhD 2013
Verena Kuhlemann, PhD 2013
Veronica Mejia-Bustamante, PhD 2013
Umberto Villa, PhD 2013
Marta D’Elia, PhD 2012
Steven Hamilton, PhD 2011
Sarah Knepper, PhD 2011
Zhuojun Tang Magnant, PhD 2011
Zhen Wang, PhD 2011
Raya Horesh, PhD 2010
Ying Wai (Daniel) Fan, PhD 2010
Piotr Wendykier, PhD 2009
Julianne Chung, PhD 2009
Nader Razouk, PhD 2008
Lauren Hanson, PhD 2007
Dawid Kurzyniec, PhD 2007
Jia Liu, PhD 2006
Kiandra Johnson, MS 2005
Katrina Palmer, PhD 2004
Lisa Perrone, PhD 2004

Data Assimilation and Parameter identification in electrophysiology

Tue, 21 Nov 2017 09:59:16 -0400

Data Assimilation is the ensemble of methods for merging data and numerical simulations when solving a specific problem. It can be pursued in different ways and for addressing different problems, from prediction to parameter identification. In this project, we specifically address the variational estimation of the conductivity parameters of the Bidomain equations. These are partial differential equations for the potential propagation in the cardiac tissue. The conductivity tensor is a critical set pf parameters with a major impact on the numerical solution. Their accurate knowledge is hard to obtain in practice. Moving from measurements of the potential on the surface of the tissue, it is possible to obtain a reliable estimate to be used in more complex problems like the optimal placement of cardiac leads. We pursue a variational approach, i.e. the minimization of the mismatch between data and simulations, constrained by the Bidomain equations or their simplified version, the Mondomain equation. As the computational costs are quite high, we need reduced models to pursue the estimation in short timelines. We work currently with approaches like Proper Orthogonal Decomposition and Proper General Decomposition.

Numerical Methods for Multispectral Tomographic Image Reconstruction

Sun, 10 Sep 2017 09:59:16 -0400

Breast cancer is the most prevalent non-skin cancer in women in the US. Although mammography is currently the most common test for the early detection and diagnosis of breast cancer, its two-dimensional nature introduces various limitations in its capabilities for advanced imaging. Over the last decade, the introduction of digital imaging technology has resulted in the development of new tomographic and pseudo-tomographic methods for imaging the breast.

Digital tomographic image reconstruction uses multiple x-ray projections obtained along a range of different incident angles to reconstruct a 3D representation of an object. For example, computed tomography (CT) generally refers to the situation when a full set of angles are used (e.g., 360 degrees) while tomosynthesis refers to the case when only a limited (e.g., 30 degrees) angular range is used. In either case, most existing reconstruction algorithms assume that the x-ray source is monoenergetic. This results in a simplified linear forward model, which is easy to solve but can result in artifacts in the reconstructed images. It has been shown that these artifacts can be reduced by using a more accurate polyenergetic assumption for the x-ray source, but the polyenergetic model requires solving a large-scale nonlinear inverse problem. In addition to reducing artifacts, a full polyenergetic model can be used to extract additional information about the materials of the object; that is, to provide a mechanism for quantitative imaging. Similar mathematical models arise when using multispectral detectors.

Bayesian Approaches for Strain Identification from Culture-Independent Samples

Wed, 27 Sep 2017 09:59:16 -0400

We develop new mathematical approaches, algorithms and systems for identifying pathogen strains using whole genome multilocus sequence typing (wgMLST) data in mixed samples. Strain identification is an underdetermined inverse problem when the samples are not cultured, i.e., contain multiple strains at unknown proportions. Therefore, we encode prior knowledge on both the strains and their proportion in a Bayesian framework. Our approaches use mixed-integer optimization to identify the most likely strains and Monte-Carlo sampling to quantify the uncertainty associated with those estimates. Motivating applications of our algorithms include the identification of P. falciparum (malaria) and E.coli (foodborne illness) strains to improve visibility and monitoring for public health officials.

Schedule 2018/19

Mon, 26 Aug 2019 09:49:04 -0400

Spring 2019 Schedule

January

1. Kelvin Kan

February

1. Zixuan Chen
1. no seminar
1. Chao Wang (University of Texas at Dallas)
1. Georgia Scientific Computing Symposium at GA tech
1. Yousef Saad (Minnesota)

March

1. SIAM CSE week, no seminar
1. Grad students research highlights
1. spring break, no seminar
1. Tom Goldstein, University of Maryland, Attacking neural networks with poison frogs: a theoretical look at adversarial examples in machine learning
1. Sung Ha Kang (GA tech)

April

1. Rencang Li (UT Arlington)
1. Mauro Perego (Sandia National Laboratory, Albuquerque)
1. Huijuan Xu
1. Derek Onken

Fall 2018 Schedule

August

1. Meet and greet + Faculty research highlights I

September

1. Faculty research highlights II + group photo
1. Sofia Guzzetti and Alessandro Barone
1. Chang Meng
1. Ru Huang

October

1. James Nagy
1. Sara Bridio (Politechnico Milano and Emory)
1. Hao-Min Zhou (GA tech), Optimal Transport on Finite Graphs with Applications
1. non-standard time and place: 10AM Atwood 215 Marta D’Elia (Sandia National Lab), Nonlocal Models in Computational Science and Engineering
1. Braxton Osting (University of Utah), Diffusion generated methods for target-valued maps
1. Colloqium: Dave Yuen (Columbia University)

November

1. Xiaojing Ye (GA State), Decentralized consensus optimization on networks with delayed and stochastic gradients
1. Blair Rossetti
1. Eldad Haber (UBC), Convolution neural networks for semantic segmentation
1. NO MEETING - Thanksgiving
1. NO MEETING

December

1. Traian Iliescu(Virginia Institute of Technology)
1. Wenjing Liao (GA tech)

Undergraduate Research Activities

Fri, 12 Oct 2018 09:49:04 -0400

Our group centrally involves undergraduate students in ongoing projects. We also provide other activities that offer excellent opportunities for undergraduate students to apply their skills to real-world problems. Interested students are encouraged to ask faculty they are interested in working with about current opportunities.

Requirements

In order to be successful, students need a strong background and interest in computational and applied mathematics and be able to commit substantial time to the research project. A critical requirement for most projects is a strong background in numerical analysis and strong programming skills as offered, e.g., in Emory’s course MATH 315. Students should also bring a lot of curiosity and enthusiasm to learn and work independently. Depending on the project, other courses or technical skills will be needed.

Schedule 2017/18

Fri, 13 Jul 2018 09:49:04 -0400

Fall 2017 Schedule

August

1. meet and greet

September

1. Alexander Viguerie
1. Clarissa Garvey and Yunyi Hu
1. Bora Ucar (LIP-ENS-LYON), On the Birkhoff–von Neumann decomposition and its use in solving sparse linear systems
1. Misha Kilmer (Tufts University), A new tensor framework - theory and applications
1. Sofia Guzzetti, Multigrid Methods for Uncertainty Propagation in (large-scale) Networks via Domain Decomposition

October

1. Arvind Krishna Saibaba (NC State University) D-optimal Experimental Design for Bayesian Inverse Problems
1. Samy Wu Fung
1. Xianqi Li (University of Florida), Backtracking-Based Accelerated Descent Methods for Large-Scale Linear Inverse Problems
1. Massimiliano Lupo Pasini

November

1. Massimiliano Marrocco-Trischitta
1. Ganesh Sundaramoorthi (KAUST) Accelerated Diffeomorphisms for Motion Estimation and Segmentation from Video
16. Special Event: John Nash Documentary, 6pm in W303
1. SIAM student chapter event

December

1. Daniel Kovari (Emory Physics)

Spring 2018 Schedule

January

1. Raya Horesh (IBM Research AI, TJ Watson Research Center) Building Energy - Modeling, Optimization and Optimal Control
1. Johannes Vorwerk (SCI Institute Utah) New methods in EEG/MEG source analysis

February

1. 4pm in W301: Colloquium: Andreas Mang (University of Houston) Computational mathematics meets medicine: Formulations, numerics, and parallel computing
1. 4pm in W301: Colloquium Kimon Fountoulakis (University of California, Berkeley) Optimization for scalable graph analytics
1. 4pm in W301: Colloquium Yuanzhe Xi (University of Minnesota) Fast and stable algorithms for large-scale computation
1. 4pm W301: Colloquium: Simona Perotto (Politecnico di Milano) When the mesh is important: The role of anisotropic mesh adaptation in numerical modeling, from crack propagation to topology optimization
1. 4pm W303: Colloquium: Erin Carson (Courant Institute, NYU) Sparse Linear Algebra in the Exascale Era
1. Lauri Mustonen, The inverse conductivity problem and how to linearize it
1. Georgia Scientific Computing Symposium at Georgia State

March

1. Eisha Nathan (GA Tech)
1. James Nagy
1. spring break -> no seminar
1. Nicola Ferro (Politecnico di Milano)
1. no seminar

April

1. 3pm E208: Colloquium: Sherry Li (Lawrence Berkeley National Laboratory)
1. no seminar
1. Yves Barbosa (Politecnico di Milano)
23 (Monday!) 4pm at W302 Pablo Blanco (Laboratório Nacional de Computação Científica, Petropolis, Brasil)
1. Colloquium: Jorge Nocedal (Northwestern University)

May

1. 2pm in W301: Yi Hong (University of Georgia) Computational and Predictive Models for Brain Imaging Studies

Wed, 06 Sep 2017 09:49:04 -0400

Our group highly values teaching and offers a comprehensive set of courses on scientific computing, applied mathematics, data science, mathematical modeling, and its applications. All our courses are taught in relatively small sizes, allowing close interactions with students.

Advanced Undergraduate Courses

MATH 315: Numerical Analysis
MATH 345: Mathematical Modeling
MATH 347: Introduction to Nonlinear Optimization
MATH 351: Partial Differential Equations
MATH 352: PDEs in Action
MATH 361&362: Probability & Statistics

Slected Special Topics Undergraduate-Level Courses

Progamming for Mathematics of Data Science (Fall 2022)
Convex Optimization (Fall 2022)

Regularly Offered Graduate-Level Courses

MATH 515: Numerical Analysis I (Numerical Linear Algebra)
MATH 516: Numerical Analysis II
MATH 517: Numerical Analysis III (Iterative Methods)
CS555: Parallel Processing
MATH 561: Matrix Analysis
MATH 571: Numerical Optimization
MATH 572: Numerical Partial Differential Equations

Selected Special Topics Graduate-Level Courses

RTG Seminar: Computational Methods and AI for Discovering New Mathematics (Fall 2023)
Introduction to Tensor Decompositions (Fall 2023)
RTG Seminar: Mathematical Research Through Model Reduction and Mixed Precision (Fall 2022)
RTG Seminar: Computational Methods for Data Science (Fall 2021)
Numerical Methods for Deep Learning (Spring 2020)
Data Assimilation (Spring 2018)
Numerical Methods for Deep Learning (Spring 2018)
Structured Matrix Computation (Fall 2017)
Bayesian Inverse Problems (Spring 2016)
Advanced Numerical Linear Algebra Methods with Applications
Fluid Dynamics

Information for Graduate Students

Wed, 06 Sep 2017 09:49:04 -0400

Why Computational and Data Enabled Science?

Computational and Data Enabled Science is at the heart of many cutting-edge technologies and demand for more precise and realistic mathematical simulations is ever growing. Thus computing powers high-impact applications such as precision medicine, medical imaging, network analysis, and machine learning. By obtaining a solid background in scientific computing, data science, and applied mathematics, students gain a highly transferable skill set in high demand both in industry and research. See also this excellent brochure.

Schedule 2016/17

Mon, 28 Aug 2017 09:49:04 -0400

Fall 2016 Schedule

August

1. Pizza, meet and greet

September

1. Clarissa Garvey
1. Yunyi Hu
1. Sofia Guzzetti
1. Massimiliano Lupo Pasini
1. Manuela Manetta

October

1. Jan Modersitzki (University of Lubeck) NOTE: This is a Thursday talk at 4:00 pm, room W201,Title and Abstract
1. Margaret Callahan
1. There will be no seminar today, to allow time to attend workshop in SOM.
1. Alessandro Barone

November

1. Lars Ruthotto
1. Michele Benzi
1. Thomas J. R. Hughes (University of Texas) NOTE: This is a Wednesday talk at 4:00 pm, room W201 Title and Abstract
1. NO MEETING - Thanksgiving

December

1. Giuliano Carlino

Spring 17 Schedule

January

1. Sundaramoorthi (KAUST): Sobolev Metrics for Optimization and Analysis in Image and Video Understanding
1. Adrien Levieux
1. Jim Nagy

February

1. Alessandro Veneziani
1. James Herring
1. Samy Wu Fung
1. Daniela Calvetti (Case Western)

March

1. No meeting: SIAM CSE Week
1. No meeting: Spring Break
1. Manuela Manetta, NOTE: This is a Thursday talk at 1:00 pm, room W303 [Title and Abstract](http://www.mathcs .emory.edu/seminar-flyers/seminar-01125.pdf)
1. Alessandro Veneziani
1. Sofia Guzzetti and Rodrigo Romarowski

April

1. Clarissa Garvey
1. Lars Ruthotto (and Becky and Ymir)
1. Francesca Arrigo (University of Strathclyde)