TRS: The Right Space

Transformations are crucial tools for mathematical modelers; for example, transforming (positive) real numbers to logarithms turns a difficult operation (multiplication) into an easier one (addition).

DARPA’s The Right Space (TRS) program seeks new mathematical/computational methods for systematically discovering such enabling transformations by leveraging advances in Scientific Machine Learning to make solving complex modeling problems easier, faster, and more interpretable.

Discovering mathematical transformations (from Fourier transforms to Inverse Scattering, and from Koopman to Bäcklund and Cole-Hopf transformations) has typically occurred through a combination of deep scientific insight/expertise and serendipity. TRS aims to (i) systematically discover new, insightful representations to solve Department of Defense-relevant problems better and faster and (ii) find and analyze the limits of the transformations’ validity.

If successful, TRS aspires to recreate, across different domains, the effect that Pierre Simon de Laplace ascribed to the invention of logarithms: By shortening the labors, [logarithms have] doubled the life of an astronomer.

Examples of Department of Defense-relevant problems that would be affected by new mathematical transformations to more useful representations may include but are not limited to:

1. Wargaming scenarios for agent-based simulations
2. Open- and closed-loop turbulent flow simulations for aerospace vehicles
3. Microstructured material mechanics for multiscale/multiphysics simulation
4. Improving the real-time accuracy of digital twins through calibration