â€¢ Computational dynamics focused on nonlinear dynamics and finite elements (e.g., a new approach for forecasting bifurcations/tipping points in aeroelastic and ecological systems, new finite element methods for thin walled beams that leads to novel reduced order models).

â€¢ Modeling nonlinear phenomena and mechano-chemical processes in molecular motor dynamics, such as motor proteins, toward early detection of neurodegenerative diseases.

â€¢ Computational methods for robotics, manufacturing, modeling multi-body dynamics, developed methods for identifying limit cycle oscillations in large-dimensional (fluid) systems.

â€¢ Turbomachinery and aeroelasticity providing a better understanding of fundamental complex fluid dynamics and cutting-edge models for predicting, identifying and characterizing the response of blisks and flade systems through integrated experimental & computational approaches.

â€¢ Structural health monitoring & sensing providing increased sensibility / capabilities by the discovery, characterization and exploitation of sensitivity vector fields, smart system interrogation through nonlinear feedback excitation, nonlinear minimal rank perturbation and system augmentation, pattern recognition for attractors, damage detection using bifurcation morphing.

Biodiversity in nature can be puzzlingly high in the light of competition between species, which arguably should eventually result in a single winner. The coexistence mechanisms that allow for this biodiversity shape the dynamics of communities and ecosystems. My research focuses on understanding the mechanisms of competitive coexistence, how competition influences community structure and diversity, and what insights observed patterns of community structure might provide about competitive coexistence.

I am interested in the use and development of data science approaches to draw insights regarding coexistence mechanisms from the structural patterns of ecological communities with respect to species’ functional traits, relative abundance, spatial distribution, and phylogenetic relatedness, through as community dynamics proceed. I am also interested in the use of Maximum Likelihood and Bayesian approaches for fitting demographic models to forest census data sets, demographic models that can then be used to quantitatively assess the role of different competitive coexistence mechanisms.

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.

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.