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

Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a major bottleneck. Although large language models can generate isolated code fragments, they lack the structured reasoning required to design, verify, and iteratively refine complete scientific pipelines. Here we introduce ATHENA, an agentic framework explicitly designed to emulate scientific research modeled as a knowledge-driven contextual bandit process. Its core loop separates conceptual policy from numerical realization through expert-derived conceptual scaffolding, enabling principled diagnosis, reformulation, and repair of computational strategies. Across scientific computing and scientific machine learning tasks, ATHENA autonomously derives and correctly applies exact analytical solutions, constructs stable numerical solvers, diagnoses ill-posed formulations, and orchestrates hybrid symbolic-numeric workflows. Quantitatively, ATHENA matches and frequently surpasses the accuracy of expert-authored reference solutions reported in the literature on canonical benchmarks. By reframing computation as an object of agentic reasoning, our framework enables autonomous orchestration of heterogeneous algorithms across scientific domains.

The convergence of large language models and agents is catalyzing a new era of scientific discovery: Agentic Science. However, common agent infrastructure is repeatedly rebuilt across scientific fields (loop fragmentation) and useful evidence and experience are lost in long-horizon research (loop discontinuity), bringing obstacles to Agentic Science at Scale. We introduce EvoMaster, a foundational evolving agent framework for Agentic Science at Scale. EvoMaster handles loop fragmentation and loop discontinuity by implementing Loop Research in which external evidence persists and improves later decisions. Through three nested loops, Execution, Exploration and Evolution (E$^3$), loop research connects research within runs, across experiments and across studies. Across ten benchmarks spanning scientific research, coding and reasoning, EvoMaster achieves the best score among four agents using GPT-5.4, reaching a mean score of 58.02%, and outperforms the strongest competing agent Codex(40.29%) while costing 35.6% less. These results show that a shared loop-research foundation can support diverse scientific agents at scale.

Recent advances in Large Language Models have fueled autonomous AI agents capable of tackling complex scientific tasks, yet existing automated research systems remain predominantly focused on empirically driven domains with quantitative benchmarks, leaving theory-driven discovery, particularly in mathematically grounded disciplines requiring rigorous proofs and synthesis of domain knowledge, largely underexplored. Key challenges include the difficulty of verifying theoretical reasoning at scale, insufficient reasoning ability for autonomous frontier exploration, and a scarcity of procedural heuristics in the literature. We introduce ReasFlow, an end-to-end autonomous agent system for reasoning-centric scientific discovery that operationalizes a collaborative paradigm where the human expert acts as Principal Investigator while the agent executes rigorous derivations as a capable graduate student. ReasFlow incorporates (i) a robust internal verification loop that audits logical coherence and corrects fundamental errors prior to human inspection, and (ii) an automated knowledge retrieval and self-improvement mechanism that proactively surfaces both declarative facts and overlooked procedural heuristics, substantially reducing expert intervention. The system unifies literature synthesis, algorithm design, theorem proving, experimentation, and manuscript preparation in a single system. Deployed to autonomously generate five complete research papers with rigorous theoretical and empirical content from minimal prompts, ReasFlow consistently achieves the highest evaluation scores among state-of-the-art open-access baselines under a curated LLM-based review rubric. ReasFlow is publicly accessible via the ReasLab platform, providing a collaborative workspace for AI-assisted theoretical research. Github repo: https://github.com/ReasLab/ReasFlow.git.