Date: 2020-09-18

Time: 15:30-16:30

Zoom Link

Meeting ID: 924 5390 4989

Passcode: 690084

Abstract:

With advances in mathematical modeling and computational methods, complex phenomena (e.g., universe formations, rocket propulsion) can now be reliably simulated via computer code. This code solves a complicated system of equations representing the underlying science of the problem. Such simulations can be very time-intensive, requiring months of computation for a single run. Gaussian processes (GPs) are widely used as predictive models for “emulating” this expensive computer code. Yet with limited training data on a high-dimensional parameter space, such models can suffer from poor predictive performance and physical interpretability. Fortunately, in many physical applications, there is additional boundary information on the code beforehand, either from governing physics or scientific knowledge. We propose a new BdryGP model which incorporates such boundary information for prediction. We show that BdryGP not only enjoys improved convergence rates over standard GP models which do not incorporate boundaries, but is also more resistant to the ``curse-of-dimensionality’’ in nonparametric regression. We then demonstrate the improved predictive performance and posterior contraction of the BdryGP model on several test problems in the literature.

This talk will feature joint work of Liang Ding, Simon Mak, C. F. Jeff Wu.

Speaker

Simon Mak is an Assistant Professor in the Department of Statistical Science at Duke University. Prior to Duke, he was a postdoctoral fellow at the Stewart School of Industrial & Systems Engineering at Georgia Tech. He has a Ph.D. in Industrial Engineering and a M.Sc. in Statistics from Georgia Tech (2018), and a B.Sc. in Statistics and Actuarial Science from Simon Fraser University (2013).

His research focuses on developing methodologies with theoretical guarantees for big data reduction and small data analytics, and applying these methods within an algorithmic workflow to solve real-world problems. His broad research interests are in engineering statistics, machine learning and experimental design, with applications to mechanical engineering, biomedical engineering, financial engineering, genetics, and signal processing.