GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms

Scientific methods are developed for classes of problems, so knowledge transfers across structurally related cases. Language-model agents can execute scientific workflows, but their problem--method relationships remain implicit, so each new problem restarts the search and little of what worked transfers. We introduce GRAFT--ATHENA, which makes this problem-to-method map explicit as an expandable probabilistic structure of admissible problems, methods, and their dependencies. Graph factorization keeps the substrate tractable, and semantic fingerprints measure similarity, so experience guides related problems. As a result, the framework matched or exceeded expert baselines, attaining near-machine-precision losses in physics-informed learning, reproducing clinically consistent blood-rheology trends, and developing a high-order hypersonic-flow solver for the Apollo Command Module that matched experimental measurements within $1.8\%$. It also proposed a certified regularization for ill-posed in vivo brain-flow reconstruction, developed a spectrally convergent physics-informed architecture, and established machine-checked universal-approximation theorems for two widely used architectures. Scientific structure enables cumulative and verifiable agentic discovery.