Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery

2026-10-02

AI Summary

This study addresses the limitation of existing numerical solvers that rely on execution-feedback-driven trial-and-error optimization, which hinders root-cause identification of performance bottlenecks. We propose ADSD, a framework adhering to a "diagnosis-first" paradigm that pioneers the integration of automated diagnosis with skill discovery. By employing AI agents to analyze failure mechanisms and encapsulate reusable numerical skills, ADSD transforms blind code editing into a structured knowledge accumulation process encompassing diagnosis, discovery, and implementation. Experimental results demonstrate that this approach significantly enhances solution accuracy and robustness across four major domains, including power flow equations. Notably, it achieves a 71-fold error reduction on the GOC-500 benchmark while exhibiting strong cross-scenario generalization capabilities.

Abstract

AI agents are becoming increasingly capable of generating scientific code, but generating code is not the same as improving the algorithms behind it. For numerical solvers, execution feedback can expose poor performance, but rarely reveals its underlying cause and how to address it. We introduce Auto-Diagnosis and Skill Discovery (ADSD), a framework that links numerical diagnosis to reusable solver self-improvement. ADSD follows a diagnosis-first paradigm that first explains why a solver performs poorly, then uses this diagnosis to guide the discovery of appropriate numerical methods. The resulting knowledge is packaged into reusable solver skills, turning solver improvement from trial-and-error editing into a structured process of diagnosis, discovery, and implementation. Across four challenging numerical domains--power flow equation, AC optimal power flow control, stiff ordinary differential equations, and heterogeneous diffusion PDEs--ADSD consistently improves solver accuracy, robustness, and efficiency. On GOC-500 power flow, for example, ADSD reduces mean solver error by nearly $71\times$, with improvements further transferring to unseen grid topologies and operating regimes.

Problem

• Numerical Intelligence
• Solver Self-Improvement
• Execution Feedback
• Numerical Diagnosis
• Scientific Code

Innovation

• Auto-Diagnosis
• Skill Discovery
• Numerical Intelligence
• Solver Self-Improvement
• AI Agents