Computational Science Qualifying Exam

Spring 2022

Committee:  Dr. Adrian Sandu (Chair); Dr. Layne Watson; Dr. Alexey Onufriev.

Timeline. Students must commit to take exam and register with the chair of the exam by Dec. 6, 2021. Students may withdraw from taking the exam by Jan. 9, 2022.

The Qualifying Exam has both a written and an oral component.

Written: Select five papers from the reading list below. For each of the papers you selected write a short (no more than one page) summary and critique of the paper in your own words. Your writeup should identify the main points or contributions of the paper, as well as the significance of the contributions. Highlight any particularly strong or weak aspects of a paper. Submit this written material to Dr. Sandu via email (sandu@cs.vt.edu) by February 1, 2022.

Oral: In February, you will make an oral presentation to the committee on two papers selected by you from the reading list. Prepare roughly 30 minutes of material. Do not provide a tutorial or short course about the details or minutiae in the papers. Your material should:

• synthesize and evaluate the importance of the main ideas and issues from the papers,
• describe how each topic is evolving (make sure you identify the main issues and developments), and
• provide your opinion on potential avenues of research that should be further explored in this sub-area.

The committee will ask questions throughout the oral exam not only regarding the two papers you chose, but on any of the papers in the list (and potential research directions).

In preparing for this exam, you should do the work yourself and should find and read any other references that seem useful. You may discuss papers in the reading list with other students who are preparing for the exam. However, you are not to work with others in preparing submissions to the exam (e.g., summaries and critiques, the talk, etc.). 

Reading List

Select five papers from the list below.

 

(1) Andre Belotto da Silva and Maxime Gazeau

A General System of Differential Equations to Model First-Order Adaptive Algorithms

Journal of Machine Learning Research 21 (2020) 1-42.

https://jmlr.org/papers/v21/18-808.html

 

(2) Charles Audet and J. E. Dennis, Jr.

SIAM J. Optim., 17(1), 188–217. (30 pages)

Mesh Adaptive Direct Search Algorithms for Constrained Optimization

Doi: 10.1137/040603371

 

(3) R. Giering and T. Kaminski. Recipes for adjoint code construction. ACM Transactions on Mathematical Software, Vol. 24, No. 4, December 1998.

Doi:10.1145/293686.293695

 

(4) J.C. Butcher

Numerical methods for ordinary differential equations in the 20th century

Journal of Computational and Applied Mathematics 125 (2000) 1–29

Doi: 10.1016/S0377-0427(00)00455-6

 

(5) D.A.Knoll and D.E.Keyes

Jacobian-free Newton–Krylov methods: a survey of approaches and applications

Journal of Computational Physics

Volume 193, Issue 2, 20 January 2004, Pages 357-397

Doi: 10.1016/j.jcp.2003.08.010

 

(6) Jean-Paul Berrut and Lloyd N. Trefethen

Barycentric Lagrange Interpolation

SIAM Review 2004, Vol. 46, No. 3, pp. 501-517

Doi: 10.1137/S0036144502417715

 

(7) Nick Bostrom

Are you living in a computer simulation?

Philosophical Quarterly (2003) Vol. 53, No. 211, pp. 243‐255.

https://www.simulation-argument.com/simulation.pdf