Bridging the gap between theoretical conceptualization and computational implementation is a major bottleneck in Scientific Computing (SciC) and Scientific Machine Learning (SciML). We introduce ATHENA (Agentic Team for Hierarchical Evolutionary Numerical Algorithms), an agentic framework designed as an Autonomous Lab to manage the end-to-end computational research lifecycle. Its core is the HENA loop, a knowledge-driven diagnostic process framed as a Contextual Bandit problem. Acting as an online learner, the system analyzes prior trials to select structural `actions' ($A_n$) from combinatorial spaces guided by expert blueprints (e.g., Universal Approximation, Physics-Informed constraints). These actions are translated into executable code ($S_n$) to generate scientific rewards ($R_n$). ATHENA transcends standard automation: in SciC, it autonomously identifies mathematical symmetries for exact analytical solutions or derives stable numerical solvers where foundation models fail. In SciML, it performs deep diagnosis to tackle ill-posed formulations and combines hybrid symbolic-numeric workflows (e.g., coupling PINNs with FEM) to resolve multiphysics problems. The framework achieves super-human performance, reaching validation errors of $10^{-14}$. Furthermore, collaborative ``human-in-the-loop" intervention allows the system to bridge stability gaps, improving results by an order of magnitude. This paradigm shift focuses from implementation mechanics to methodological innovation, accelerating scientific discovery.

翻译：弥合理论概念化与计算实现之间的鸿沟是科学计算（SciC）与科学机器学习（SciML）中的一个主要瓶颈。我们提出了ATHENA（用于分层进化数值算法的智能体团队），这是一个设计为自主实验室的智能体框架，用于管理端到端的计算研究生命周期。其核心是HENA循环，这是一个以情境赌博问题为框架的知识驱动诊断过程。系统作为在线学习者，通过分析先前的试验，在专家蓝图（例如，通用逼近定理、物理信息约束）的指导下，从组合空间中选择结构性“动作”（$A_n$）。这些动作被转化为可执行代码（$S_n$）以生成科学奖励（$R_n$）。ATHENA超越了标准自动化：在SciC中，它能自主识别数学对称性以获得精确解析解，或在基础模型失败时推导稳定的数值求解器。在SciML中，它执行深度诊断以处理不适定问题，并结合混合符号-数值工作流（例如，将PINNs与FEM耦合）来解决多物理场问题。该框架实现了超人类性能，验证误差达到$10^{-14}$。此外，通过协作式“人在回路”干预，系统能够弥合稳定性差距，将结果提升一个数量级。这一范式转变将重点从实现机制转向方法论创新，从而加速科学发现。