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Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery

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Briefings

This article presents Auto-Diagnosis and Skill Discovery (ADSD), a framework linking numerical diagnosis to reusable solver self-improvement. ADSD follows a diagnosis-first paradigm, explaining solver performance issues before guiding the discovery of appropriate numerical methods. Across four challenging domains including power flow, AC optimal power flow, stiff ODEs, and heterogeneous diffusion PDEs, ADSD consistently improves solver accuracy, robustness, and efficiency. On the GOC-500 power flow benchmark, ADSD reduced mean solver error by nearly 71 times, with improvements transferring to unseen grid topologies and operating regimes.

Key points

• ADSD is a framework that links numerical diagnosis to reusable solver self-improvement by following a diagnosis-first paradigm.
• ADSD consistently improves solver accuracy, robustness, and efficiency across four challenging numerical domains including power flow, AC optimal power flow, stiff ODEs, and heterogeneous diffusion PDEs.

Context and limitations

The study covers four specific numerical domains and uses the GOC-500 power flow benchmark; results may not generalize to all solver types or domains.

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