My areas of interest are control, estimation, and optimization, with applications to energy systems in transportation, automotive, and marine domains. My group develops model-based and data-driven tools to explore underlying system dynamics and understand the operational environments. We develop computational frameworks and numerical algorithms to achieve real-time optimization and explore connectivity and data analytics to reduce uncertainties and improve performance through predictive control and planning.
My research involves developing novel data collection strategies and image reconstruction techniques for Magnetic Resonance Imaging. In order to accelerate data collection, we take advantage of features of MRI data, including sparsity, spatiotemporal correlations, and adherence to underlying physics; each of these properties can be leveraged to reduce the amount of data required to generate an image and thus speed up imaging time. We also seek to understand what image information is essential for radiologists in order to optimize MRI data collection and personalize the imaging protocol for each patient. We deploy machine learning algorithms and optimization techniques in each of these projects. In some of our work, we can generate the data that we need to train and test our algorithms using numerical simulations. In other portions, we seek to utilize clinical images, prospectively collected MRI data, or MRI protocol information in order to refine our techniques.
We seek to develop technologies like cardiac Magnetic Resonance Fingerprinting (cMRF), which can be used to efficiently collect multiple forms of information to distinguish healthy and diseased tissue using MRI. By using rapid methods like cMRF, quantitative data describing disease processes can be gathered quickly, enabling more and sicker patients can be assessed via MRI. These data, collected from many patients over time, can also be used to further refine MRI technologies for the assessment of specific diseases in a tailored, patient-specific manner.
Our work is interdisciplinary in nature and we connect three fields, chemistry, physics and materials science. Our goal is to develop theoretical tools that give access to directly experimentally relevant quantities. We develop and apply codes that describe two types of electronic motion (i) weakly correlated electrons originating from the delocalized “wave-like” s- and p-orbitals responsible for many electron correlation effects in molecules and solids that do not contain transition metal atoms (ii) strongly correlated electrons residing in the d- and f-orbitals that remain localized and behave “particle-like” responsible for many very interesting effects in the molecules containing d- and f-electrons (transition metal nano-particles used in catalysis, nano-devices with Kondo resonances and molecules of biological significance – active centers of metalloproteins). The mutual coupling of these two types of electronic motion is challenging to describe and currently only a few theories can properly account for both types of electronic correlation effects simultaneously.
Available research projects in the group involve (1) working on a new theory that is able to treat weakly and strongly correlated electrons in molecules with multiple transition metal centers with applications to molecular magnets and active centers of enzymes (2) developing a theory for weakly correlated electrons that is able to produce reliable values of band gaps in semiconductors and heterostructures used in solar cells industry (3) applying the QM/QM embedding theories developed in our group to catalysis on transition metal-oxide surfaces and (4) applying the embedding formalism to molecular conductance problems in order to include correlation effects.
My research is mainly concerned with theoretical and computational hydrodynamics, with applications in nonlinear ocean wave prediction and dynamics, wave-body interactions, and wave turbulence theory. I have incorporated the data science tools in my research, especially in the following two projects:
1. Quantification of statistics of extreme ship motions in irregular wave fields: In this project, we propose a new computational framework that directly resolves the statistics (and causal factors) of extreme ship responses in a nonlinear wave field. The development leverages a range of physics and learning based approaches, including nonlinear wave simulations (potential flow), ship response simulations (e.g., CFD), dimension-reduction techniques, sequential sampling, Gaussian process regression (Kriging) and multi-fidelity methods. The key features of the new approach include (i) description of the stochastic wave field by a low-dimensional probabilistic parameter space, and (ii) use of minimum number of CFD simulations to provide most information for converged statistics of extreme motions.
2. Real-time wave prediction with data assimilation from radar measurements: In this project, we develop the real-time data assimilation algorithm adapted to the CPU-GPU hardware architecture, to reduce the uncertainties associated with radar measurement errors and environmental factors such as wind and current in the realistic ocean environment. Upon integration with advanced in-situ or remote wave sensing technology, the developed computational framework can provide heretofore unavailable real-time forecast capability for ocean waves.
The long temporal and large spatial scales of ecological systems make controlled experimentation difficult and the amassing of informative data challenging and expensive. The resulting sparsity and noise are major impediments to scientific progress in ecology, which therefore depends on efficient use of data. In this context, it has in recent years been recognized that the onetime playthings of theoretical ecologists, mathematical models of ecological processes, are no longer exclusively the stuff of thought experiments, but have great utility in the context of causal inference. Specifically, because they embody scientific questions about ecological processes in sharpest form—making precise, quantitative, testable predictions—the rigorous confrontation of process-based models with data accelerates the development of ecological understanding. This is the central premise of my research program and the common thread of the work that goes on in my laboratory.
Current research includes a project funded by Toyota that uses Markov Models and Machine Learning to predict heart arrhythmia, an NSF-funded project to detect Acute Respiratory Distress Syndrome (ARDS) from x-ray images and projects using tensor analysis on health care data (funded by the Department of Defense and National Science Foundation).
Dr. Lee’s research in data science concerns biological questions in systems biology and network medicine by developing algorithms and models through a combination of statistical/machine learning, information theory, and network theory applied to multi-dimensional large-scale data. His projects have covered genomics, transcriptomics, proteomics, and metabolomics from yeast to mouse to human for integrative analysis of regulatory networks on multiple molecular levels, which also incorporates large-scale public databases such as GO for functional annotation, PDB for molecular structures, and PubChem and LINCS for drugs or small compounds. He previously carried out proteomics and metabolomics along with a computational derivation of dynamic protein complexes for IL-3 activation and cell cycle in murine pro-B cells (Lee et al., Cell Reports 2017), for which he developed integrative analytical tools using diverse approaches from machine learning and network theory. His ongoing interests in methodology include machine/deep learning and topological Kolmogorov-Sinai entropy-based network theory, which are applied to (1) multi-level dynamic regulatory networks in immune response, cell cycle, and cancer metabolism and (2) mass spectrometry-based omics data analysis.
Erhan Bayraktar, PhD, the holder of the Susan Smith Chair, is a full professor of Mathematics at the University of Michigan, where he has been since 2004. Professor Bayraktar’s research is in stochastic analysis, control, applied probability and mathematical finance. He has over 120 publications in top journals in these areas.
Professor Bayraktar is recognized as a leader in his areas of research: he is a corresponding editor in the SIAM Journal on Control and Optimization and also serves in the editorial boards of Applied Mathematics and Optimization, Mathematics of Operations Research, Mathematical Finance. His research has been also been continually funded by the National Science Foundation; in particular, he received a CAREER grant.
Professor Bayraktar has also been devoting his time to teaching and synergistic activities: Professor Bayraktar has been the director of the Risk Management and Quantitative Finance Masters program since its inception in 2015. As one of the two organizers of the Financial/Actuarial Math seminar which brings about 10-15 speakers every academic year and he has also organized several international workshops in stochastic analysis for finance and insurance in Ann Arbor.
Areas of interest: Mathematical finance, applied probability, stochastic analysis, stochastic control, optimal stopping.
Professor Saigal has held faculty positions at the Haas School of Business, Berkeley and the department of Industrial Engineering and Management Sciences at Northwestern University, has been a researcher at the Bell Telephone Laboratories and numerous short term visiting positions. He currently teaches courses in Financial Engineering. In the recent past he taught courses in optimization, and Management Science. His current research involves data based studies of operational problems in the areas of Finance, Transportation, Renewable Energy and Healthcare, with an emphasis on the management and pricing of risks. This involves the use of data analytics, optimization, stochastic processes and financial engineering tools. His earlier research involved theoretical investigation into interior point methods, large scale optimization and software development for mathematical programming. He is an author of two books on optimization and large set of publications in top refereed journals. He has been an associate editor of Management Science and is a member of SIAM, AMS and AAAS. He has served as the Director of the interdisciplinary Financial Engineering Program and as the Director of Interdisciplinary Professional Programs (now Integrative Design + Systems) at the College of Engineering.
Professor Seiford’s research interests are primarily in the areas of quality engineering, productivity analysis, process improvement, multiple-criteria decision making, and performance measurement. In addition, he is recognized as one of the world’s experts in the methodology of Data Envelopment Analysis. His current research involves the development of benchmarking models for identifying best-practice in manufacturing and service systems. He has written and co-authored four books and over one hundred articles in the areas of quality, productivity, operations management, process improvement, decision analysis, and decision support systems.