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David Bortz
Professor in Applied Mathematics
Friday, Feb. 6 | 10:40 a.m. | AERO 114

Abstract: The creation and inference of mathematical models is central to modern scientific discovery. As more realism is demanded of models, however, the conventional framework of science-guided model proposal, discretization, parameter estimation, and model refinement becomes unwieldy, expensive, and computationally daunting. Recent advances in Weak form-based Scientific Machine Learning (WSciML) allow for the creation and inference of interpretable models directly from data via advanced numerical functional analysis, computational statistics, and numerical linear algebra techniques. This class of methods completely bypasses the need for forward-solve numerical discretizations and yields both parsimonious mathematical models and efficient parameter estimates. These methods are orders of magnitude faster and more accurate than traditional approaches and far more robust to the high noise levels. The combination of these features in a single framework provides a compelling alternative to both traditional modeling approaches as well as modern black-box neural networks. In this talk, I will present our weak form approach, describing our equation learning (WSINDy) and parameter estimation (WENDy) algorithms. I will demonstrate these performance properties via applications to several canonical problems in structured population modeling, cell migration, and mathematical epidemiology.

Biography: Prof. Bortz earned his PhD in 2002 with H.T. Banks at North Carolina State ³Ô¹ÏÍø. After a postdoc in Mathematics at the ³Ô¹ÏÍø of Michigan, he joined the faculty in Applied Math at the ³Ô¹ÏÍø of Colorado in 2006. The core of his research interests is scientific computing methods for data-driven modeling and inverse problems at the intersection of applied mathematics and statistics. His group has been developing a Weak-form Scientific Machine Learning framework with a wide range of applications to biology and medicine (wound healing, microbiology, epidemiology, ecology, etc.) and, more recently, to computational plasma physics in the context of fusion. His research has received support from NSF, NIH, DOE, and DOD.