NSF Research Training Group in Applied Differential Equations and Scientific Computing

Andrea Bertozzi, Principal Investigator

This Research Training Group supports undergraduates and beginning graduate students doing research in applied differential equations and scientific computing. The group is a consortium of students from UCLA, Harvey Mudd College and from additional universities. This web page gives an overview and research results for the REU portion of the program.

This program is run with the philosophy that there a number of ways to effectively involve undergraduates in research that gives them a meaningful experience beyond the classroom. Being at a large research university like UCLA allows for many modalities of interaction. Bringing students from four year colleges to UCLA allows them to have an experience working alongside PhD students and postdocs that they would not obtain in their college environment. In some cases, we place individual students in regular research groups where they can contribute a valuable role that is suitable for their level of experience yet contributes ultimately to part of a research paper. In other instances, we have formed small focus groups with a single faculty mentor working together with a small team of undergraduates. The latter type of group is modelled somewhat on the IPAM RIPS program but where the research projects are suggested by UCLA faculty members rather than by corporations. Finally, we have benefitted from interdisciplinary interactions through the Applied Mathematics Laboratory which bring together students, postdocs, and faculty in engineering and science to work on problems where mathematics can make a significant impact. The possibility of having students work on hands-on experiments provides a larger array of research opportunities suitable for students at the undergraduate level.

In addition to providing a valuable research experience for undergraduates, we try to heavily involve young faculty, postdocs, and advanced PhD students in the mentoring process, while maintaining oversight by senior faculty. These interactions provides the REU students with a viewport into the steps needed to develop a research career. Moreover, it provides invaluable mentoring experience for our junior researchers, often enabling them to advance their careers through broader access to tenure track positions and through additional research publications and products brought about by projects involving the undergraduate researchers.

While NSF RTG support is crucial for funding the undergraduates, to maintain a program of this size and scope, we are indebted to support from regular research grants through a number of agencies, including NSF, ARO, ONR, DOE, NIH, other DoD support, and some industrial partners. The large majority of support for faculty mentors and PhD students assisting with this program comes from these regular research grants.


Here is a recent article on undergraduate research. It is based on studies that were largely done at four year colleges, rather than at research universities.

What Good Is Undergraduate Research, Anyway? , The Chronicle of Higher Education, Aug. 17, 2007.


Mentors 2006

Mentors 2007

Mentors 2008

List of Undergraduate Participants, Summer 2006

List of Undergraduate Participants, Summer 2007

List of Undergraduate Participants, Summer 2008


Harvey Mudd student projects in this program

Selected reports, papers, presentations and videos

2007 REU projects

  • Trevor Ashley 2007 - Boundary estimation and video tracking , powerpoint presentation and video clips
  • Arash Fayz and Ying Vuong 2007 - Crime modelling and data, powerpoint presentation
  • Meiching Fong 2007 - Dimension reduction on hyperspectral images, presentation and report
  • Zhong Hu 2007 - Gradient Free Boundary Tracking, presentation and report
  • Vicknesh Selvam 2007 - Hyperspectral TV Denoising and Inpainting, presentation and report
  • Kenn Tevin 2007 - Realistic movement of burglars in crime simulation code, PDF presentation
  • Ani Asatryan, Kate Jaffe, Tracy Nguyen, and Ilina Sandler, MATLAB Implementation of Statistical Condition Estimation, faculty advisors- Alan J. Laub and Jianlin Xia

    2006 REU projects

  • Jeffrey Hyman 2006 - Report on Monte Carlo Sampling - includes personal critique of the summer REU program.

  • Jon Azose 2006 - Video of crime hotspots on Jeff Brantingham's website

  • Jason Reich 2006 - preprint in preparation

    Jason Reich, Xiaobin Niu, Young-Ju Lee, Russel Caflisch, and Christian Ratsch, Lateral and Vertical Segregation in Thin Alloy Films, in preparation.

  • Asher Metchik 2006 - publication

    Thomas Ward and Asher Metchik, Viscous fluid mixing in a tilted tank by periodic shear, Chemical Engineering Science, 62 (22), 6274-6284.

  • James von Brecht 2006 - publication

    James H. von Brecht, Seshadri R. Thiruvenkadam, and Tony F. Chan, Occlusion tracking with Logic Models , IASTED Conference on Signal and Image Processing 2007

  • Vlad Voroninski and Abhijeet Joshi 2006 - publication

    Y. Landa, D. Galkowski, Y. R. Huang, A. Joshi, C. Lee, K. K. Leung, G. Mall a, J. Treanor, V. Voroninski, A. L. Bertozzi, and R. Tsai, Robotic path planning and visibility with limited sensor data, in the proceedings of the 2007 American Control Conference.

  • Vlad Voroninski and Abhijeet Joshi 2006 - publication

    Kevin K. Leung, Chung H. Hsieh, Yuan R. Huang, Abhijeet Joshi, Vlad Voroninski, and Andrea L. Bertozzi, A second generation micro-vehicle testbed for cooperative control and sensing strategies, in the proceedings of the 2007 American Control Conference.

  • Wyatt Toolson 2006 - paper published

    Chad M. Topaz, Andrew J. Bernoff, Sheldon Logan, and Wyatt Toolson, A model for rolling swarms of locusts European Physical Journal, vol. 157, pages 93-109, 2008.

  • Ani Asatryan, Vatche Attarian, Abhijeet Joshi, Vlad Voroninski, Meghdi Aboulian, and Krystle McBride 2006 - paper published

    Carmeliza Navasca, Ani Asatryan, Vatche Attarian, Abhijeet Joshi, Vlad Voroninski, Meghdi Aboulian, and Krystle McBride Implementations of control laws for motion camouflage in a pursuit-evasion system , Proceedings of the 23rd IFIP Conference on System Modeling and Optimization, Krakow, Poland 2007.