SURE offers insight and learning in some of the hottest topics in data science and computational mathematics through hands-on research experiences. Learn to work as a team member by interacting with graduate students and faculty, and gain an understanding as to what it takes to conduct real-world research.
An eight-week SURE program will be hosted in hybrid mode in the summer of 2022. SURE researchers will receive a stipend of $500 per week. The applicants are required to have a foundational background in mathematics (calculus, differential equations, and linear algebra) and some programming skills. If you are interested in the program, please use this form (a Gmail account is needed) to apply for the program. If you have any questions regarding the program, please feel free to email Computing-REU@iit.edu.
Summer 2022 projects
Project Title: Data Science and Dynamical Systems
Description: Data is noisy. Data evolves with time. Data science and dynamical systems are naturally hand in hand. We will develop algorithms to gain insights into, and to predict evolution of dynamical systems from engineering and science, based on observed data sets.
Project Title: Speedier Simulations
Adviser: Fred Hickernell
Description: Monte Carlo methods are used to solve problems involving uncertainty, such as financial risk and physical models whose parameters are not known precisely. The QMCPy research group, https://qmcpy.org, is developing and implementing algorithms in an open source Python package that speed up Monte Carlo simulations. Students will contribute to QMCPy by exploring new use cases, by implementing new algorithms, and/or by improving performance through parallel processing. By joining the QMCPy research group, students will experience teamwork, learn to identify and solve research problems, follow good practices in technical software development, and hone their communication skills. A background in statistics and Python (or other language) programming will be an advantage.
Project Title: Generalized Linear Regression via Variational Inference Approach
Aim: The aim of this project is to create new variational inference generalized linear models. Generalized linear regression models are among the most important supervised learning models, which provide analytical prediction and inference for various kinds of data. Variational inference is an important area in the field of machine learning. Combining the two approaches together, the main idea of this project is to convert the inference problem into an optimization problem via minimizing a certain functional so as to approximate the target posterior distribution derived from the Bayesian generalized linear models.
Prerequisites: Proficient programming using R or Python. Entry to medium level of knowledge on statistics, probability, computational mathematics.
Students will learn Bayesian framework, generalized linear models, variational inference, and some other important topics in machine learning that are involved in the background of this project.
Students will learn how to code for larger scale simulation examples and implement the various machine learning algorithms and apply them on real-world examples.
Students will learn how to write academic papers that aim for journal publications.
Project Title: From the Formation of Snowflakes to Crystal Growth
Adviser: Shuwang Li
Description: Crystal growth is a classical example of a phase transformation from the liquid phase to the solid phase via heat transfer. For example, water becomes ice if heat is removed by decreasing the temperature. The solidification process is very important because material properties, such as electrical conductivity, mechanical ductility, and strength, are determined by the microstructures formed during phase transformations. Therefore, it is essential to know how crystals evolve during solidification and what kinds of geometric patterns they can form. As early as the 1600s, Johannes Kepler, a well-known astronomer, was amazed by the beauty of snowflakes and tried to understand this symmetry. While Kepler did not know about crystalline symmetry, he did have the insight that the symmetry of snowflakes (shown in the Figure) may be derived from a facultas for matrix (i.e. morphogenetic field or some inherent properties). In this project, students will learn the underlying physics of snowflake formation and evolution. In particular, students will be exposed to the general concepts of mathematical modeling and hands-on scientific computing.