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Mathematical Analysis and Modeling

We perform research in applied mathematics, mathematical modeling, numerical analysis, and scientific computing for application to multidisciplinary problems of interest to the NIST measurement science program.

The group applies expertise in mathematical subdisciplines such as differential equations, nonlinear dynamics, inverse and ill-posed problems, continuous optimization, and image analysis.  Application areas include materials modeling, computational electromagnetics and acoustics, electro-optics, fluid mechanics, fracture and deformation, nanotechnology, and systems biology.  In collaboration with NIST and outside scientists, our researchers develop and analyze mathematical and computational models, methods, and tools necessary for the fundamental understanding of physical, biological, and information systems and processes.  We work with academia, industry, professional societies, consortia, and standards bodies on measurement science issues related to the modeling of such applications.

News and Updates


G2Aero: A Python package for separable shape tensors

Olga Doronina, Zachary J. Grey, Andrew Glaws
G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes

Noise-resilient deep tomographic imaging

Zhen Guo, Zhiguang Liu, George Barbastathis, Qihang Zhang, Michael Glinsky, Bradley Alpert, Zachary H. Levine
X-ray tomography is a non-destructive imaging technique that reveals the interior of an object from its projections at different angles. Under limited-angle and

Separable Shape Tensors for Aerodynamic Design

Zachary J. Grey, Andrew Glaws, Olga Doronina
Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape

Physics-assisted Generative Adversarial Network for X-Ray Tomography

Zhen Guo, Jungki Song, George Barbastathis, Michael Glinsky, Courtenay Vaughan, Kurt Larson, Bradley Alpert, Zachary H. Levine
X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials study