Colloquium Artificial Intelligence - Dr. Anton van Beek, University of Dublin

Title: Designing with Non-Differentiable and Discontinuous Functions

Abstract:

Machine learning has proven to be a powerful tool to expedite scientific and engineering discoveries in a plethora of disciplines but is often incompatible/inefficient when used in conjunction with systems that have non-differentiable discontinuous behavior (especially when data is sparse). This is a substantial limitation as many contemporary scientific and engineering challenges involve functions with these characteristics (e.g., contact problems in mechanics, and material properties because of phase changes). Dr. van Beek holds the belief that this class of problems requires a rigorous Bayesian treatment to expedite and facilitate discovery. Consequently, in this talk, he will start with a general introduction to Bayesian methods in the context of engineering design and science. Subsequently, he will introduce the discontinuous Gaussian process (DCGP) model that involves learning a parametric, yet flexible, function to ensure that the residuals of a training data set are continuous, differentiable, and jointly normally distributed. Subsequently, he will demonstrate the potential of the DCGP model for three applications: i) global emulation of discontinuous and non-differentiable responses, ii) design when the locations of discontinuity boundaries are known a priori, and iii) design when the locations of the discontinuity boundaries are unknown. The latter scenario is particularly interesting as this holds the potential to expedite, and sometimes enable, the discovery of properties that emerge from unknown interactions within a system being studied (e.g., high-entropy alloys that form new crystal structures at specific volumetric ratios). The talk will conclude by exploring open research challenges, and avenues for continued scientific inquiry.

Biography:

Anton van Beek is a Lecturer/Assistant Professor in the School of Mechanical and Materials Engineering at University College Dublin. As the principal investigator of the optimization and data of the designed systems laboratory (ODDS-Lab), he studies statistical methods that enable the design of increasingly more complex systems. He received his B.S. (2013) in Mechanical Engineering from the HZ University of Applied Sciences (The Netherlands). Afterward, he worked for one year as a naval architect at IHC Merwede. He then returned to graduate school and received his M.S. (2017) in Mechanical Engineering from the University of Michigan and Shanghai Jiao Tong University Joint Institute (China). Finally, he completed his Ph.D. (2021) under the supervision of Dr. Wei Chen at the Mechanical Engineering Department of Northwestern University (United States). Anton has (co-)authored 27 peer- reviewed research manuscripts (17 journal papers, 9 conference papers, and 1 book chapter).