Albert S. Berahas is an Assistant Professor in the department of Industrial & Operations Engineering. His research broadly focuses on designing, developing and analyzing algorithms for solving large scale nonlinear optimization problems. Such problems are ubiquitous, and arise in a plethora of areas such as engineering design, economics, transportation, robotics, machine learning and statistics. Specifically, he is interested in and has explored several sub-fields of nonlinear optimization such as: (i) general nonlinear optimization algorithms, (ii) optimization algorithms for machine learning, (iii) constrained optimization, (iv) stochastic optimization, (v) derivative-free optimization, and (vi) distributed optimization.
Alex Gorodetsky’s research is at the intersection of applied mathematics, data science, and computational science, and is focused on enabling autonomous decision making under uncertainty. He is especially interested in controlling, designing, and analyzing autonomous systems that must act in complex environments where observational data and expensive computational simulations must work together to ensure objectives are achieved. Toward this goal, he pursues research in wide-ranging areas including uncertainty quantification, statistical inference, machine learning, control, and numerical analysis. His methodology is to increase scalability of probabilistic modeling and analysis techniques such as Bayesian inference and uncertainty quantification. His current strategies to achieving scalability revolve around leveraging computational optimal transport, developing tensor network learning algorithms, and creating new multi-fidelity information fusion approaches.
Sample workflow for enabling autonomous decision making under uncertainty for a drone operating in a complex environment. We develop algorithms to compress simulation data by exploiting problem structure. We then embed the compressed representations onto onboard computational resources. Finally, we develop approaches to enable the drone to adapt, learn, and refine knowledge by interacting with, and collecting data from, the environment.
My main interest is theoretical statistics as implied to complex model from semiparametric to ultra high dimensional regression analysis. In particular the negative aspects of Bayesian and causal analysis as implemented in modern statistics.
An analysis of the position of SCOTUS judges.
I study the percolation model, which is the model for long-range connectivity formation in systems that include polymerization, flow in porous media, cell-phone signals, and the spread of diseases. I study this on random graphs and other networks, and on regular lattices in various dimensions, using computer simulation and analysis. We have also worked on developing new algorithms. I am currently applying these methods to studying the COVID-19 pandemic, which also requires comparison with some of the vast amount of data that is available from every part of the world.
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).