Machine learning, at its heart, is the process of learning from examples. However, in many scientific domains, we not only have training data or examples from which to learn, but also physical models of either the data collection mechanism or the underlying physical phenomenon. In this talk, I will describe two settings in which physical models can be incorporated within a machine learning framework to yield improved predictive performance. First, we will consider using training data to help solve ill-posed linear inverse problems such as deblurring, deconvolution, inpainting, compressed sensing, and superresolution. Recent advances in machine learning and image processing have illustrated that it is often possible to learn a regularizer from training data that can outperform more traditional regularizers. We will see that whether or how a forward model is leveraged can significantly impact how many training samples are needed to achieve a target accuracy. Second, we will examine using a combination of observational data and simulated data to improve subseasonal climate forecasts. Treating both types of data as co-equal training samples can bias many learning methods and yield misleading results. I will describe an alternative framework that combines observational data with a correlation graph that can be estimated from large ensemble climate model outputs, and we will see how this approach leads to more accurate forecasts. Finally, we will discuss open problems and future directions at the intersection of machine learning and the physical sciences.
Rebecca Willett is a Professor of Statistics and Computer Science at the University of Chicago. Her research interests include network and imaging science with applications in medical imaging, wireless sensor networks, astronomy, and social networks. Prof. Willett completed her PhD in Electrical and Computer Engineering at Rice University. Prior to joining the University of Chicago, she held the position of Assistant and Associate Professor in the Electrical and Computer Engineering department at Duke University and then the position of Associate professor in the Electrical and Computer Engineering department at the University of Wisconsin-Madison. She has received several awards, including the National Science Foundation CAREER Award and the Air Force Office of Scientific Research Young Investigator Program award. She has also held numerous visiting researcher positions which include the Pure and Applied Mathematics at UCLA, the University of Wisconsin-Madison, the French National Institute for Research in Computer Science and Control (INRIA), and the Applied Science Research and Development Laboratory at GE Medical Systems (now GE Healthcare.