Defense Advanced Research Projects AgencyTagged Content List

Mathematics

Ultimate truth

Showing 62 results for Math RSS
Complex, nonlinear, multiscale dynamical systems are ubiquitous. Examples include weather, fluids, materials, biological systems, communication networks, and social systems. These systems often evolve to a critical state built up from a series of irreversible and unexpected events, which severely limits development and implementation of mathematical models to accurately predict formation and evolution of patterns in such systems.
The explosive growth of global digital connectivity has opened new possibilities for designing and conducting social science research. Once limited by practical constraints to experiments involving just a few dozen participants-often university students or other easily available groups-or to correlational studies of large datasets without any opportunity for determining causation, scientists can now engage thousands of diverse volunteers online and explore an expanded range of important topics and questions.
The exponential growth of diverse science data represents an unprecedented opportunity to make substantial advances in complex science and engineering, such as discovery of novel materials or drugs. However, without tools to unify principles, results, models and other kinds of data into a single computational representation, it is difficult to relate data from any one scientific problem or area to the broader body of knowledge.
New manufacturing technologies such as additive manufacturing have vastly improved the ability to create shapes and material properties previously thought impossible. Generating new designs that fully exploit these properties, however, has proven extremely challenging. Conventional design technologies, representations, and algorithms are inherently constrained by outdated presumptions about material properties and manufacturing methods. As a result, today’s design technologies are simply not able to bring to fruition the enormous level of physical detail and complexity made possible with cutting-edge manufacturing capabilities and materials.
Successful integration of next generation AI into DoD applications must be able to deal with incomplete, sparse and noisy data as well as unexpected circumstances that might arise while solving real world problems. Thus, there is a need for new computing models that are efficient and robust, can learn new concepts with very few examples, and can guide the development of adequate novel hardware to support them.
| AI | Algorithms | Math |