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

2026-05-11

AI Summary

Current scientific agents lack cross-task knowledge accumulation and struggle to evolve continuously. This work proposes the GRAFT framework, which structures combinatorial decision spaces via factorized probabilistic trees to enable method transfer and autonomous expansion of action spaces. Integrating a large language model–driven planner, solver, and evaluator with graph reduction, Bayesian networks, and physics-informed machine learning, GRAFT reduces parameter complexity from exponential to linear. It further introduces a method fingerprint metric space to support algorithmic self-evolution. Evaluated on the PIML benchmark and challenging engineering tasks—including hypersonic flow reconstruction and hemorheological inversion—the system surpasses both human experts and existing agents, autonomously discovering novel numerical methods such as exponentially convergent spectral PINNs.

Abstract

Scientific discovery can be modeled as a sequence of probabilistic decisions that map physical problems to numerical solutions. Recent agentic AI systems automate individual scientific tasks by orchestrating LLM-driven planners, solvers, and evaluators. Each method is a combination of methodological actions, with many viable combinations for any given problem and structural dependencies between choices. However, existing frameworks treat each problem in isolation, with no shared substrate to accumulate methodological experience across domains. Here we show that GRAFT-ATHENA, a self-improving agentic framework, learns from past problems and autonomously expands its own action space across diverse domains. GRAFT (Graph Reduction to Adaptive Factored Trees) projects combinatorial decision spaces into factored probabilistic trees in which each method is a single path, taking the parameter footprint from exponential to linear. In the lineage of classical Bayesian networks, the factorization is an $I$-map of the policy, and the resulting paths embed as unique fingerprints in a metric space whose closeness lets each new problem learn from similar past ones. On canonical physics-informed machine learning (PIML) benchmarks, GRAFT-ATHENA improves over human and prior agentic baselines, and on production solvers, it tackles complex engineering problems such as reconstructing Mach-10 flow over the Apollo Command Module from a 1968 report and recovering shear-thinning blood-cell rheology. Notably, the system grows its own knowledge substrate, autonomously proposing regularization constraints for ill-posed inverse problems and discovering new numerical methods such as a spectral PINN with exponential convergence. These results provide a foundation for autonomous laboratories that grow more capable with every problem they solve.

Problem

• scientific discovery
• agentic AI
• methodological experience
• cross-domain learning
• autonomous problem solving

Innovation

• self-improving agentic framework
• Graph Reduction to Adaptive Factored Trees
• probabilistic decision trees
• physics-informed machine learning
• autonomous algorithm discovery