ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

2025-12-03

AI Summary

A persistent gap exists between theoretical formulations and computational implementations in scientific computing (SciC) and scientific machine learning (SciML), hindering automated discovery of mathematical structure and robust numerical solution. Method: This paper introduces HENA, a closed-loop intelligent agent framework that models algorithmic evolution as a contextual bandit problem. It integrates domain expertise (e.g., physical constraints, approximation principles), online learning, combinatorial optimization, PINN–FEM coupling, and executable code generation to construct a hierarchical team of evolutionary agents. The framework enables automatic symmetry discovery, synthesis of stable numerical solvers, and hybrid symbolic–numerical co-solving across multiphysics domains, with human-in-the-loop intervention to overcome stability bottlenecks. Contribution/Results: Experiments demonstrate verification accuracy up to 10⁻¹⁴ on canonical SciC benchmarks—surpassing hand-crafted expert solutions—and a further order-of-magnitude improvement under human–agent collaboration.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Adversarial Agents
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Agentic search
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

Abstract

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.

Problem

• Bridge theoretical conceptualization and computational implementation in SciC/SciML
• Autonomously manage end-to-end computational research lifecycle
• Diagnose and resolve ill-posed formulations and multiphysics problems

Innovation

• Agentic framework autonomously manages computational research lifecycle
• Knowledge-driven diagnostic loop selects actions via contextual bandit problem
• Hybrid symbolic-numeric workflows resolve multiphysics problems autonomously