Dr. Kochunas’s research focus is on the next generation of numerical methods and parallel algorithms for high fidelity computational reactor physics and how to leverage these capabilities to develop digital twins. His group’s areas of expertise include neutron transport, nuclide transmutation, multi-physics, parallel programming, and HPC architectures. The Nuclear Reactor Analysis and Methods (NURAM) group is also developing techniques that integrate data-driven methods with conventional approaches in numerical analysis to produce “hybrid models” for accurate, real-time modeling applications. This is embodied by his recent efforts to combine high-fidelity simulation results simulation models in virtual reality through the Virtual Ford Nuclear Reactor.
His research interest lies in the intersection of signal processing, data science, machine learning, and numerical optimization. He is particularly interested in computational methods for learning low-complexity models from high-dimensional data, leveraging tools from machine learning, numerical optimization, and high dimensional geometry, with applications in imaging sciences, scientific discovery, and healthcare. Recently, he is also interested in understanding deep networks through the lens of low-dimensional modeling.
Dr. Gen Li is an Assistant Professor in the Department of Biostatistics. He is devoted to developing new statistical methods for analyzing complex biomedical data, including multi-way tensor array data, multi-view data, and compositional data. His methodological research interests include dimension reduction, predictive modeling, association analysis, and functional data analysis. He also has research interests in scientific domains including microbiome and genomics.
My research focuses on the development of novel Magnetic Resonance Imaging (MRI) technology for imaging the heart. We focus in particular on quantitative imaging techniques, in which the signal intensity at each pixel in an image represents a measurement of an inherent property of a tissue. Much of our research is based on cardiac Magnetic Resonance Fingerprinting (MRF), which is a class of methods for simultaneously measuring multiple tissue properties from one rapid acquisition.
Our group is exploring novel ways to combine physics-based modeling of MRI scans with deep learning algorithms for several purposes. First, we are exploring the use of deep learning to design quantitative MRI scans with improved accuracy and precision. Second, we are developing deep learning approaches for image reconstruction that will allow us to reduce image noise, improve spatial resolution and volumetric coverage, and enable highly accelerated acquisitions to shorten scan times. Third, we are exploring ways of using artificial intelligence to derive physiological motion signals directly from MRI data to enable continuous scanning that is robust to cardiac and breathing motion. In general, we focus on algorithms that are either self-supervised or use training data generated in computer simulations, since the collection of large amounts of training data from human subjects is often impractical when designing novel imaging methods.
My research interest lies in applying data science for actionable transformation of human health from the bench to bedside. Current research focus areas include cutting edge single-cell sequencing informatics and genomics; precision medicine through integration of multi-omics data types; novel modeling and computational methods for biomarker research; public health genomics. I apply my biomedical informatics and analytical expertise to study diseases such as cancers, as well the impact of pregnancy/early life complications on later life diseases.
Cyber-security is a complex and multi-dimensional research field. My research style comprises an inter-disciplinary (primarily rooted in economics, econometrics, data science (AI/ML/Bayesian and Frequentist Statistics), game theory, and network science) investigation of major socially pressing issues impacting the quality of cyber-risk management in modern networked and distributed engineering systems such as IoT-driven critical infrastructures, cloud-based service networks, and app-based systems (e.g., mobile commerce, smart homes) to name a few. I take delight in proposing data-driven, rigorous, and interdisciplinary solutions to both, existing fundamental challenges that pose a practical bottleneck to (cost) effective cyber-risk management, and futuristic cyber-security and privacy issues that might plague modern (networked) engineering systems. I strongly strive for originality, practical significance, and mathematical rigor in my solutions. One of my primary end goals is to conceptually get arms around complex, multi-dimensional information security and privacy problems in a way that helps, informs, and empowers practitioners and policy makers to take the right steps in making the cyber-space more secure.
Our research aims to address fundamental problems in both biomedical research and computer science by developing new tools tailored to rapidly emerging single-cell omic technologies. Broadly, we seek to understand what genes define the complement of cell types and cell states within healthy tissue, how cells differentiate to their final fates, and how dysregulation of genes within specific cell types contributes to human disease. As computational method developers, we seek to both employ and advance the methods of machine learning, particularly for unsupervised analysis of high-dimensional data. We have particular expertise in manifold learning, matrix factorization, and deep learning approaches.
Today’s real-world problems are complex and large, often with overwhelmingly large number of unknown variables which render them doomed to the so-called “curse of dimensionality”. For instance, in energy systems, the system operators should solve optimal power flow, unit commitment, and transmission switching problems with tens of thousands of continuous and discrete variables in real time. In control systems, a long standing question is how to efficiently design structured and distributed controllers for large-scale and unknown dynamical systems. Finally, in machine learning, it is important to obtain simple, interpretable, and parsimonious models for high-dimensional and noisy datasets. Our research is motivated by two main goals: (1) to model these problems as tractable optimization problems; and (2) to develop structure-aware and scalable computational methods for these optimization problems that come equipped with certifiable optimality guarantees. We aim to show that exploiting hidden structures in these problems—such as graph-induced or spectral sparsity—is a key game-changer in the pursuit of massively scalable and guaranteed computational methods.
My research lies at the intersection of optimization, data analytics, and control.
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.