The Defense Advanced Research Projects Agency (DARPA) Defense Sciences Office (DSO) is issuing a Disruption Opportunity (DO) under the Program Announcement for Disruptioneering, DARPA-PA-24-04 Amendment 1. This funding opportunity, titled "The Right Space (TRS)," invites submissions of innovative research concepts focused on developing mathematical methods for systematically discovering useful mathematical transformations. These transformations aim to enhance modeling efficiency by making complex problems easier, faster, and more interpretable. The opportunity targets research in scientific machine learning (SciML) to create computationally efficient, interpretable, and generalizable solutions applicable to Department of Defense (DoD) challenges.

DARPA seeks novel mathematical frameworks that can optimize system variable transformations to improve computational modeling across domains such as agent-based simulations, aerospace turbulence modeling, microstructured material mechanics, and real-time digital twin calibration. The research effort is divided into two phases: Phase 1 (Feasibility Study) and Phase 2 (Proof of Concept). The total funding limit for both phases is $1,250,000, with Phase 1 capped at $500,000 and Phase 2 at $750,000. Each phase is expected to last 12 months, with a combined maximum period of 24 months. Awards will be made under the Other Transaction (OT) for Prototype project authority.

Applicants must select one of four mathematical system classes: (i) discrete interactions (e.g., agent-based models, complex networks), (ii) continua (e.g., ordinary or partial differential equations), (iii) transformations between stochastic systems, or (iv) calibration between models. Proposals must outline a notional target application within the chosen class, demonstrate its relevance to the DoD, establish a baseline comparison to the state-of-the-art (SotA), and describe how SciML techniques will enhance modeling performance. Additionally, proposals must include justifications with calculations, projections, and theoretical estimations to support claims of feasibility and performance improvements.

The TRS program establishes strict performance milestones. Phase 1 will focus on developing a mathematical transformation, understanding its validity limits, and demonstrating generalizability within a system class. Phase 2 will extend the work by applying the transformation to new instances, generalizing across system classes, and validating model performance through government evaluation. Success metrics include a reduction in floating-point operations (FLOP) by 100-1000x at 99% accuracy, an extension of transformation validity by at least 10x beyond SotA, and systematic generalization across modeling domains.

The submission process consists of an optional Abstract phase followed by a full proposal submission. Abstracts, due by March 24, 2025, provide proposers with feedback but are not mandatory for full proposal consideration. Full proposals must be submitted electronically via the DARPA Broad Agency Announcement (BAA) Portal by May 2, 2025, at 4:00 p.m. Eastern Time. Proposals must adhere to the content and format requirements outlined in DARPA-PA-24-04 and the accompanying cost buildup workbook. Awards are expected to be issued within 118 days of the announcement’s posting date (March 4, 2025), with an anticipated program start date of July 1, 2025.

All questions related to the TRS DO should be directed to TRS@darpa.mil. Additional resources, including FAQs, will be available on the TRS DARPA website. For those new to DARPA funding, a free resource through DARPAConnect provides guidance on doing business with the agency, including understanding Broad Agency Announcements.