Alex Gorodetsky is an Assistant Professor in the Department of Aerospace Engineering. His research includes using applied mathematics and computational science to enhance autonomous decision making under uncertainty. His research has an emphasis on controlling systems that must act in complex environments that are often represented through expensive computational simulations. His research uses tools from wide ranging areas including uncertainty quantification, statistical inference, machine learning, numerical analysis, function approximation, control, and optimization. Several of the key areas he focuses on are: optimal planning by solving large scale Markov decision processes, fast Bayesian estimation for nonlinear dynamical systems, high-dimensional compression and approximation of physical quantities of interest, and fusion of information from varying simulation fidelities and data through multi-fidelity modeling.
Heather Mayes is an Assistant Professor in the Department of Chemical Engineering. Her research group uses multi-scale modeling to discover protein-sugar interactions and to harness them for renewable energy and improved health. The study of carbohydrate-protein interactions is an important step to create renewable fuels and chemicals from non-food biomass, and the results can be applied to several human diseases, including cancer and autoimmune disorders. Prof. Mayes uses computational tools in her research, including quantum mechanics, molecular dynamics, and rare-event sampling methods. She collaborates with experimental groups to understand past and guide future wet-lab studies to advance renewable chemicals and fuels, as well as disease understanding.
Brian Denton is a Professor in the Department of Industrial & Operations Engineering, and a member of the Institute for Healthcare Policy and Innovation. His primary research interests are in optimization under uncertainty with applications to medical decision-making. He uses stochastic programming, simulation-optimization and Markov decision processes to optimize decisions regarding detection, treatment, and prevention of chronic diseases, including cancer, diabetes and heart disease.
Eric Michielssen is a Professor of Electrical Engineering and Computer Science – Electrical and Computer Engineering Division and Associate Vice President for Advanced Research Computing.
His research interests include all aspects of theoretical, applied, and computational electromagnetics, with emphasis on the development of fast (primarily) integral-equation-based techniques for analyzing electromagnetic phenomena. His group studies fast multipole methods for analyzing static and high frequency electronic and optical devices, fast direct solvers for scattering analysis, and butterfly algorithms for compressing matrices that arise in the integral equation solution of large-scale electromagnetic problems.
Furthermore, the group works on plane-wave-time-domain algorithms that extend fast multipole concepts to the time domain, and develop time-domain versions of pre-corrected FFT/adaptive integral methods. Collectively, these algorithms allow the integral equation analysis of time-harmonic and transient electromagnetic phenomena in large-scale linear and nonlinear surface scatterers, antennas, and circuits.
Recently, the group developed powerful Calderon multiplicative preconditioners for accelerating time domain integral equation solvers applied to the analysis of multiscale phenomena, and used the above analysis techniques to develop new closed-loop and multi-objective optimization tools for synthesizing electromagnetic devices, as well as to assist in uncertainty quantification studies relating to electromagnetic compatibility and bioelectromagnetic problems.
In a strategic environment, agents face decisions where the outcomes depend on the behavior of other autonomous agents. The strategic reasoning group develops techniques for understanding and engineering complex multiagent environments, using concepts and methods from economics as well as computer science. Specifically, we apply game-theoretic principles to data from large-scale agent-based simulation, in an approach called empirical game-theoretic analysis (EGTA). EGTA combines simulation, machine learning, and other empirical methods to reason about the strategic issues in complex multiagent settings. We are particularly interested in domains characterized by dynamism, networks, and uncertainty, including applications in financial markets, information security, and sustainable transportation.
Prof. Shen’s research derives multifaceted mathematical optimization models for decision making under data uncertainty and information ambiguity. The models she considers often feature stochastic parameters and discrete (0-1) decision variables. The goal is to seek optimal solutions for balancing risk and cost objectives associated with complex systems. She also develops efficient algorithms for solving the large-scale optimization models, based on integer programming, stochastic and data-driven approaches, and special network topologies. In particular, her research has been applied to cyberinfrastructure design and operations management problems related to power grids, transportation, and Cloud Computing systems.
Ann Jeffers is an Associate Professor in the Department of Civil and Environmental Engineering. Her research seeks to use computational methods to study structural performance under fire hazards. Jeffers’ work has particularly focused on coupling a high-resolution CFD fire model to a low resolution structural model to study structural performance under natural fire effects. The coupled fire-structure simulation has necessitated the formulation of novel finite elements and algorithms to bridge the disparities between the fire and structural domains. She has also conducted research using probabilistic methods (i.e., Monte Carlo simulation and analytical reliability methods) to study the propagation of uncertainty and evaluate the reliability of structural systems threatened by fire.
Prof. Duraisamy is interested in the development of computational models, algorithms and uncertainty quantification approaches with application to fluid flows. This research includes fluid dynamic modeling at a fundamental level as well as in an integrated system-level setting. An overarching theme in his research involves the use of simulation and data-driven methods to answer scientific and engineering questions with an appreciation of the effect of modeling uncertainties on the predicted results. Prof. Duraisamy’s group is also interested in developing numerical algorithms to operate on evolving computational architectures such as GPUs. He is the Director of the Center for Data-Driven Computational Physics.
Fidkowski’s research interests lie in the development of robust, scalable, and adaptive solvers for computational fluid dynamics. Target applications include steady and unsteady convection dominated flows, such as those observed in external aerodynamics. Quantitative numerical error estimates for these problems are important for vehicle analysis and design; however they are challenging to obtain, especially for multi-dimensional simulations involving complex physical models running on parallel architectures. Fidkowski’s group is applying adjoint-based error estimation techniques to these problems, with the goal of generating tailored meshes for the prediction of selected outputs of interest. Research topics under investigation include improving effectivity of error estimates, applying error estimation to novel discretizations, combining error estimation with uncertainty quantification and optimization, and diversifying adaptation mechanics, especially for high-order unsteady simulations on deformable domains.
His research group aims to develop computational and mathematical techniques to address various aspects of materials behavior, which exhibit complexity and structure on varying length and time scales. The work draws ideas from quantum mechanics, statistical mechanics and homogenization theories to create multi-scale models from fundamental principles, which provide insight into the complex behavior of materials. Topics of research include developing multi-scale methods for density-functional theory (electronic structure) calculations at continuum scales, electronic structure studies on defects in materials, quasi-continuum method, analysis of approximation theories, numerical analysis, and quantum transport in materials.