Overview: DARPA/DSO has issued an ARC Opportunity inviting submissions of abstracts for innovative exploratory research concepts in the technical domain of mathematics (https://www.darpa.mil/ARC). ARC Opportunities are designed to allow an individual researcher the opportunity and time to focus on nascent, paradigm-shifting ideas for national security applications. This COMPASS Opportunity is issued under the umbrella ARC Exploration Announcement (EA), DARPA-EA-25-02.

Proposers are encouraged to submit abstracts as early as possible. The submission period ends on 12 May 2025. Abstracts submitted to this ARC Opportunity will be evaluated on a rolling basis. Funding for this ARC Opportunity is limited. Should funding be exhausted, the Government may elect to shorten the overall submission period with an amendment to this ARC Opportunity.

More details regarding the funding opportunity can be found on sam.gov. Please ensure you scroll down to the: attachments/Link section to review the PDFs titled “DARPA-EA-25-02-03” and “Original Solicitation: DARPA-EA-25-02- Advanced Research Concepts (ARC)”.

Background: Mathematics is a pillar of national security. A decision-maker’s ability to synchronize military activities across five domains (air, land, maritime, space, and cyberspace), and adapt to rapidly changing threat landscapes hinges on robust mathematical frameworks and effective problem formulations that fully encapsulate the complexities of real-world operational environments. Unfortunately, many existing mathematical approaches in Defense rely on “good-enough” approximations, resulting in fragile solutions that severely limit our nation’s ability to address these evolving challenges in future conflicts. In contrast, establishing robust mathematical frameworks and properly formulating problems can yield profound and wide-reaching results. To excel in increasingly complex, dynamic, and uncertain operational environments, military decision-makers need richer mathematical frameworks that fully capture the intricacies of these challenges. Emerging fields in mathematics offer the potential to provide these frameworks, but realizing their full potential requires innovative problem formulations.

Solicitation Question: How can new mathematical frameworks enable paradigm shifting problem formulations that better characterize complex systems, stochastic processes, and random geometric structures?

Scope: The COMPASS ARC Opportunity seeks proposals that leverage new mathematical frameworks to develop novel problem formulations for Defense applications. Of particular interest are problem formulations that exploit recent mathematical advancements in complex systems and modern probability (such as graph signal processing, random geometric graphs, graphons, mean field theory, McKean-Vlasov processes, random matrices/tensors, rough path theory, stochastic partial and ordinary differential equations on manifolds, stochastic geometry, etc.) to address one or more of the following problem classes:

• Heterogeneous and multiscale behavior in large systems or networks.
• Stochastic processes in dynamic, random, or information-limited environments.
• Random geometric structures in high dimensions.

Examples of relevant DoD application areas include, but are not limited to, supply chains, infrastructure or human systems, distributed networks, resource allocation, contested communications or sensor networks, intelligence analysis, multi-domain operations (air, land, maritime, space, and cyberspace), mission planning, information domain awareness, target tracking, or swarming and cooperative control.