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

arXiv:2605.11117v3 Announce Type: replace Abstract: Language-model agents plan, execute, and evaluate scientific workflows. However, the problem--method relationships guiding their choices remain implicit, so plausible outputs can violate the assumptions of the scientific problem. We introduce Graph Reduction to Adaptive Factored Trees (GRAFT), which makes this problem-to-method map explicit as an expandable probabilistic structure of admissible problems, methods, and dependencies. Because this structure follows scientific semantics, knowledge from documentation, papers, and domain experts can be encoded, while factorization keeps the structure tractable. Semantic fingerprints of encoded problems measure their similarity, so expertise and experience guide related problems. GRAFT-guided workflows exceeded published expert baselines in physics-informed learning, recovered blood-rheology trends, predicted Apollo Command Module hypersonic loading within 1.8\% of experiment, and established machine-checked error bounds for regularized brain-flow reconstruction and a spectral physics-informed architecture. The representation retains evaluated outcomes and incorporates new methods, allowing scientific knowledge and experience to accumulate.