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Mathematical Modeling and Optimization

Abstractions, modeling, control, and design
Manifolds of a censored loss function; adapted from Khan, Larson, Wild, SIAM Optimization, forthcoming.

Argonne’s Mathematics and Computer Science Division is developing models, theory, algorithms, and scalable implementations to build a rigorous mathematical foundation for addressing scientific and engineering challenges.

Our research in partial differential equations focuses on the development and numerical analysis of scalable algorithms for solving systems involving complex multiphysics, multiscale phenomena. Our work in mathematical modeling includes strong multidisciplinary research projects encompassing linear algebra, adjoint-based techniques, and uncertainty quantification for stochastic systems.

Our optimization research involves development of new mathematical formulations, underlying theory, and methods for solving optimization problems arising in control, data assimilation, experimental design, inverse problems, and machine learning. Such problems include mixed-integer optimization, optimization under uncertainty, derivative-free optimization, multilevel optimization, complementarity problems, and optimization applied to game theoretic models.