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

arXiv: https://arxiv.org/abs/2605.11117 · HTML: https://mlsanity.com/paper/2605.11117/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 18 of its 147 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)
- Synthetic data and self-improvement for LLMs / [Self-evolving LLM agents](https://mlsanity.com/synth/self-evolving-llm-agents/)

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [AIDE: AI-Driven Exploration in the Space of Code](https://mlsanity.com/paper/2502.13138/) (2025)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [CodePDE: An Inference Framework for LLM-driven PDE Solver Generation](https://mlsanity.com/paper/2505.08783/) (2025)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems](https://mlsanity.com/paper/2601.22401/) (2026)
- [PINNsAgent: Automated PDE Surrogation with Large Language Models](https://mlsanity.com/paper/2501.12053/) (2025)
- [Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework](https://mlsanity.com/paper/2510.05158/) (2025)
- [Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks](https://mlsanity.com/paper/2604.05230/) (2026)
- [GraphAgents: Knowledge Graph-Guided Agentic AI for Cross-Domain Materials Design](https://mlsanity.com/paper/2602.07491/) (2026)
- [AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing](https://mlsanity.com/paper/2602.17607/) (2026)
- [ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2512.03476/) (2025)
- [PDE-Agent: A toolchain-augmented multi-agent framework for PDE solving](https://mlsanity.com/paper/2512.16214/) (2025)
- [HARDMath2: A Benchmark for Applied Mathematics Built by Students as Part of a Graduate Class](https://mlsanity.com/paper/2505.11774/) (2025)
- [AutoNumerics-Zero: Automated Discovery of State-of-the-Art Mathematical Functions](https://mlsanity.com/paper/2312.08472/) (2023)
- [Higher-Order Knowledge Representations for Agentic Scientific Reasoning](https://mlsanity.com/paper/2601.04878/) (2026)

## Built on by (most cited first, 6 of 6)

- [Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks](https://mlsanity.com/paper/2606.20467/) (2026)
- [Workflow Closure Is Not Scientific Closure in Auto-Research Systems](https://mlsanity.com/paper/2605.26200/) (2026)
- [Physics-Audited Agentic Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2607.07379/) (2026)
- [Learning to Choose: An Empowerment-Guided Multi-Agent System with semantic communication for Adaptive Method Selection](https://mlsanity.com/paper/2605.30042/) (2026)
- [Quantifying the biophysical properties of stomatocytes in health and disease](https://mlsanity.com/paper/2606.05227/) (2026)
- [LLM-IDEA: Identifiability-Driven Experimental Agent for Autonomous Discovery of Mechanistic World Models](https://mlsanity.com/paper/2610.11253/) (2026)

## Abstract (arXiv)

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.