Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery
ADSD diagnoses weak numerical solvers and cuts GOC-500 error by nearly 71 times.
Auto-Diagnosis and Skill Discovery (ADSD) links numerical diagnosis to reusable solver improvement: it first explains why a solver performs poorly, then uses that diagnosis to discover numerical methods and package them as skills. The authors evaluate it on power-flow equations, AC optimal power flow, stiff ordinary differential equations, and heterogeneous diffusion PDEs. On GOC-500 power flow, ADSD reduces mean solver error by nearly 71 times, and gains transfer to unseen grid topologies and operating regimes.
- ADSD diagnoses why a numerical solver fails before proposing methods.
- Discovered methods are packaged as reusable solver skills.
- Tested on power flow, AC optimal power flow, stiff ODEs, and PDEs.
- On GOC-500, mean solver error falls by nearly 71 times.
Full article161 words · extracted from huggingface.co · click to collapse
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 71times, with improvements further transferring to unseen grid topologies and operating regimes.
Text extracted automatically; images, tables and formatting may be missing. Original: https://huggingface.co/papers/2610.03872