Abstract:
I will start with an overview of the research portfolio of my lab, which spans the range from the discovery of high-performance materials to biomedical devices to combustion engines and electric motors to smart buildings and extra-terrestrial habitats. The common factor across all these applications is building predictive models by combining existing physical knowledge (differential equations and symmetries) with noisy data. Depending on the application, such predictive models are essential for designing better artifacts, optimizing manufacturing processes, detecting and diagnosing faults, short-term control, and long-term planning. Mathematically, these problems are smoothing and calibration problems involving physical fields (e.g., strains, stresses, temperatures, pressures) that satisfy partial differential equations with potentially unknown initial and boundary conditions, uncertain parameters, random external excitations, or even missing physics. I will briefly review my group’s work on solving these problems, focusing on high-dimensional stochastic partial differential equations and nonlinear, parametric magnetostatics using physics-informed neural networks. After highlighting some of the drawbacks of these approaches, I will propose a unifying Bayesian framework inspired by statistical field theory (i.e., statistical mechanics of continuum field quantities). The framework relies on constructing a prior probability measure on the space of physical fields that assigns higher probability to fields that satisfy the physical equations. It conditions this prior measure on the available data via a stochastic model of the measurement process, i.e., a likelihood. I will elaborate on the theoretical foundations of this proposal and provide numerical evidence in its support.
Ilias Bilionis
Biographical note:
Bilionis obtained his Diploma in Applied Mathematics and Physical Sciences from the National Technical University of Athens in 2008. In 2013, he obtained his Ph.D. in Applied Mathematics from Cornell University. After graduation, he spent a year working as a postdoctoral researcher at the Mathematics and Computer Science Division of Argonne National Laboratory. In August 2014, he became an Assistant Professor of Mechanical Engineering at Purdue University, where he established the Predictive Science Laboratory (PSL). The mission of of PSL is to create artificial intelligence technologies that accelerate the pace of engineering innovations. The applications of PSL span the range between technical systems (e.g., electric machines, high-performance materials, medical devices) and sociotechnical systems (e.g., smart buildings, extra-terrestrial habitats). His research is highly interdisciplinary and has been funded by NSF, NASA, DARPA, and several industrial grants (Cummins, Eli Lilly, Ford Motor Company, Facebook). Bilionis’ has published 60 journal papers, 2 book chapters, and 24 conference papers. In 2019 Bilionis was presented with the “Outstanding Faculty Mentor of Mechanical Engineering Graduate Students” award for his service as a graduate student mentor. Bilionis has developed the course “ME 539 Introduction to Scientific Machine Learning” the goal of which is to teach data science to engineers. The class uses active learning to combine lectures with hands-on, in class computational activities and is now available through edX. The course has been offered six times already and a total of about 500 graduate students across the college of engineering have taken it. Bilionis is also responsible for designing and developing a data science course for the core mechanical engineering curriculum. He has received the “Outstanding Engineering Teacher Recognition” three times.