Professor Burns' current research is focused on computational methods for modeling, control, estimation and optimization of complex systems where spatially distributed information is essential. This includes systems modeled by partial and delay differential equations. Recent applications include modeling and control of thermal fluids, design and thermal management systems and optimization of mobile sensor networks.
Professor Chung's research concerns computational methods in the intersection of computational modeling, machine learning, data analytics with an emphasis on inverse problems. Driven by its application, he and his group develop and analyze efficient numerical methods for inverse problems. Applications of interest are, but not limited to, systems biology, medical and geophysical imaging, and dynamical systems.
Professor Gugercin studies computational mathematics, numerical analysis, and systems and control theory with a focus on data-driven modeling and model reduction of large-scale dynamical systems with applications to inverse problems, structural dynamics, material design, and flow control.
Professor Hewett's research interests lie at the intersection of inverse problems, deep learning, and high-performance computing. His research is motivated by problems in science with extreme data and compute scales, for example geoscience and space physics. Research in these areas also involves developments in numerical differential equations, optimization, estimation, and statistics.
Professor Klaus' research mainly concerns the spectral theory of linear operators and their connection with nonlinear evolution equations. This research has applications in the study of optical pulse propagation.
Professor Tao Lin's main research interest is the numerical analysis on computational methods related with differential equations. He designs new numerical methods and carry out their convergence analysis. His recent research focuses on immersed finite element (IFE) methods that can solve interface problems of partial differential equation with interface independent meshes. He is also working on applying IFE methods to interface inverse problems via the shape optimization methodology.
Dr. Martin is an assistant professor doing research focused on computational mathematics, particularly with applications to geosciences. Her interests include data-intensive high performance computing, signal processing, imaging science, inverse problems, and working with large-scale sensor networks collecting streaming data.
Professor Warburton holds the John K. Costain Chair in the College of Science at Virginia Tech and is a faculty member of both the Department of Mathematics and the Computational Modeling and Data Analytics program. His research interests include developing new parallel algorithms and methods that are used to solve PDE based physical modes on the largest supercomputers.