Department of Mathematical Sciences, George Mason University
Tuesday, March 16, 2021, 3:00 PM EST (1:00 PM MST)
A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.
Abstract: Recently there has been renewed interest in learning forecast operators from time series data. In the deterministic case this problem is equivalent to learning a map, and machine learning methods such as kernel regression, deep networks, and reservoir computers have been adapted to this problem. When the problem is stochastic, or if one is interested in uncertainty quantification, the goal is to learn the forward operator. Whether learning a map or an operator, choosing a machine learning method involves choosing: (1) a basis, (2) a regularizer, and (3) an optimization scheme. In this talk we explore the existing techniques in terms of these three choices and focus in particular on the choice of basis. We show that for a large class of stochastic systems on manifolds, the Diffusion Maps algorithm approximates the optimal basis. Next, we consider methods to combine a model-free method with an imperfect model in order to overcome model error. In particular, we discuss some developing applications to multi-sensor arrays including calibration and drift compensation.
Bio: Tyrus Berry received his PhD from George Mason University in 2013 studying dynamical systems and manifold learning under Timothy Sauer. He then spent a fruitful two years at Pennsylvania State University as a postdoc working with John Harlim before returning to George Mason as a postdoc in 2015. He is currently an assistant professor at George Mason University where he continues to focus on manifold learning research with applications to dynamical systems.
Host: Günay Doğan
Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)