Summary
Algorithms are sequences of finite computational steps that transform an input into an output; good ones make intractable modeling problems tractable. Breakthrough numerical algorithms that enable applications are typically discovered through both serendipity and the wisdom/lifetime dedication of an expert scientist
Algorithm discovery has thus typically been limited by human inspiration and available data. Recently, researchers have developed methods to automatically discover algorithms for particular instances of well-known problems, yet these instances do not directly generalize to nearby problems (e.g., different sizes, different geometries, different equations)..
The Mathematics for the Discovery of Algorithms and Architectures (DIAL) Disruption Opportunity will develop methods to discover new generalizable numerical algorithms in a principled way to make DoD critical computations tractable. The goal of DIAL is to develop disruptive capabilities in computer-aided algorithm discovery via optimization for enabling applications. Examples of defense-relevant applications that need new and better algorithms involve multiple space/time scales and multiphysics modeling.
These include, but are not limited to, determining flow transitions and transport at high MACH numbers; designing and controlling properties of materials with complex microstructures; and managing multiscale supply chain risks.