Skip to main content
Mathematics and Computer Science Division

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.

 

CONTACT US

Mathematics and Computer Science General Inquiries

info@mcs.anl.gov
Related Project

Preparing PETSc/TAO for Exascale

We are developing and extending PETSc/TAO in two crucial directions: simulations (that require algebraic solvers and/or time integrators) at the exascale and optimization at the exascale utilizing coupled ensembled simulations.

Related Project

Exascale Computing in the MCS Division

Accelerating delivery of an exascale computing ecosystem to provide breakthrough modeling and simulation to address the nation’s most critical challenges

Related Project

HEP Data Analytics on HPC

Developing and deploying new tools and algorithms to enable HPC facilities to meet new data analysis demands

Related Project

Preparing PETSc/TAO for Exascale

We are developing and extending PETSc/TAO in two crucial directions: simulations (that require algebraic solvers and/or time integrators) at the exascale and optimization at the exascale utilizing coupled ensembled simulations.