Computational Science Qualifying Exam

Spring 2021

Committee:  Dr. Adrian Sandu (Chair),   Dr. Layne Watson,  Dr. Anuj Karpatne.

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

Written: For each of the papers on the reading list 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 7, 2021.

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

 

1.     Sahani Pathiraja and Sebastian Reich. DISCRETE GRADIENTS FOR COMPUTATIONAL BAYESIAN INFERENCE. Journal of Computational Dynamics, Volume 6, Number 2, pp. 385-400, 2019. doi: 10.3934/jcd.2019019.

 

2.     Sebastian Reich. Data assimilation: The Schrodinger perspective. Acta Numerica, pp. 635–711, 2019, doi:10.1017/S0962492919000011.

 

3.     Alessio Spantini, R. Baptista, Y. Marzouk. Coupling techniques for nonlinear ensemble filtering, 2019. https://arxiv.org/pdf/1907.00389.pdf.

 

4.     Adrian Sandu and Tianfeng Chai. Chemical Data Assimilation—An Overview. Atmosphere 2011, 2, 426-463; doi:10.3390/atmos2030426.

 

5.     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

 

6.     M.Raissi, P.Perdikaris, G.E.Karniadakis.  Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378 (2019) 686–707 doi: 10.1016/j.jcp.2018.10.045.

 

7.     Yinhao Zhu and Nicholas Zabaras. Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification. Journal of Computational Physics, 366:415–447, 2018. doi: 10.1016/j.jcp.2018.04.018

 

8.     F.Regazzoni, L.Dedè, A.Quarteroni. Machine learning for fast and reliable solution of time-dependent differential equations. Journal of Computational Physics, Volume 397, 15 November 2019, 108852. doi: 10.1016/j.jcp.2019.07.050.

 

9.     Liu Yang, Xuhui Meng, George Em Karniadakis. B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data, 2020. https://arxiv.org/abs/2003.06097.