# Applied Mathematics

The Applied Mathematics research program in ASCR develops the mathematical and scientific computing foundations to accelerate the pace of DOE scientific discoveries. In its nearly 60 year history, the program has made significant advances in applied mathematics that have been essential enablers of modern computational science. The mathematical software libraries and research developments are the basis for many of the insights and discoveries made from using the high-performance computers on which the codes are run. Funding from this program has assisted generations of graduate and postdoctoral students who have continued on to contribute productively to research organizations in industry, universities, and federal laboratories. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used in ways that could only be imagined at the program’s inception.

The following are key components of the overall Applied Mathematics research program:

**Core Applied Mathematics areas.**Optimization, linear algebra, uncertainty quantification (UQ), differential equations, machine learning (ML), meshes, multigrid, reduced order models**Scientific Software**. High performance solvers (PETSc, Trilinos, Nek5000), automatic differentiation, parallel-in-time integrators, adaptive meshes**Multifaceted Math Center themes.**Science at user facilities, power grid, additive printing, material design**Core workforce programs**. Lab base program, DOE Early Career, Lab fellowships, university grants**Workshops.**Scientific Machine Learning, Multifaceted Mathematics, Exascale Applied Mathematics, Analysis of Petascale Data