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Project: Machine Learning for Physical Systems
Much of machine learning is focused on recognizing patterns and making predictions based on training data. However, in many physical science settings, the complexity of the task is too high for effective learning giving the amount of available data. In these settings, it is essential to incorporate knowledge of the underlying physical system to mitigate the effect of limited data. Examples include using a combination of training data and models of a CT scanners operation to develop better medical image reconstruction methods, leveraging both observational and simulated data to develop better climate predictions, and building deep learning-based surrogate models for computationally demanding PDE-based simulators of physical systems. While there are isolated examples of successes in these regimes, little is known on a fundamental level. What are optimal machine learning methods that leverage both training data and physical models? How does sample complexity scale with the type of physical system and the accuracy of our models? Which kinds of PDE models are most amenable to deep surrogate models? This project will focus on developing new methodology and theory for machine learning for physical system that will address these and other open problems.

Mentor: Rebecca Willett, Professor, Statistics, Computer Science, and the College

Rebecca Willett is a Professor of Statistics and Computer Science at the University of Chicago. Her research is focused on machine learning, signal processing, and large-scale data science. She completed her PhD in Electrical and Computer Engineering at Rice University in 2005 and was an Assistant then tenured Associate Professor of Electrical and Computer Engineering at Duke University from 2005 to 2013. She was an Associate Professor of Electrical and Computer Engineering, Harvey D. Spangler Faculty Scholar, and Fellow of the Wisconsin Institutes for Discovery at the University of Wisconsin-Madison from 2013 to 2018. Willett received the National Science Foundation CAREER Award in 2007, is a member of the DARPA Computer Science Study Group, and received an Air Force Office of Scientific Research Young Investigator Program award in 2010. Willett has also held visiting researcher or faculty positions at the University of Nice in 2015, the Institute for Pure and Applied Mathematics at UCLA in 2004, the University of Wisconsin-Madison 2003-2005, the French National Institute for Research in Computer Science and Control (INRIA) in 2003, and the Applied Science Research and Development Laboratory at GE Healthcare in 2002.