Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery
Peter Chen, Wotao Yin
University of California, Berkeley · DAMO Academy, Alibaba Group U.S.
Published October 2, 2026 · on the feed October 6, 2026 · ▲ 9 · arXiv 2610.03872
The 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 71times, with improvements further transferring to unseen grid topologies and operating regimes.
The Brief
2:04A short podcast summary of the paper. Written and voiced by AI.
Transcript
Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery. By Peter Chen and one other, from the University of California, Berkeley and DAMO Academy, Alibaba Group. Published on the second of October. No code repository is linked to it.
AI agents are getting more capable at writing scientific code. But generating code is not the same thing as improving the algorithm behind it. For numerical solvers the difference is sharp. Execution feedback can show that a solver performs poorly, yet it rarely reveals the underlying cause, or how to address it. Without a cause to work from, improving a solver comes down to trial-and-error editing.
Auto-Diagnosis and Skill Discovery, or ADSD, is a framework that links numerical diagnosis to reusable solver self-improvement. Its paradigm is diagnosis first. Before anything is changed, the framework explains why the solver is performing poorly. Only then does that explanation guide the discovery of numerical methods suited to the problem it found.
What gets discovered is not left as a one-off fix. The resulting knowledge is packaged into reusable solver skills. Solver improvement stops being a sequence of edits and becomes a structured process with three stages: diagnosis, discovery, and implementation. Each stage hands the next something specific, a cause and then a method, rather than a bare signal that the output was bad.
The framework is tested across four challenging numerical domains: the power flow equation, AC optimal power flow control, stiff ordinary differential equations, and heterogeneous diffusion PDEs. Across them, ADSD consistently improves solver accuracy, robustness and efficiency. The example the authors single out is GOC-500 power flow, where ADSD cuts mean solver error by nearly seventy-one times. Those improvements carry over further, to grid topologies and operating regimes that were not seen.
Diagnosis before repair: that ordering is the whole proposal. An agent that knows why a solver fails can go looking for the right method, and once a method is found, it becomes a skill to reach for again rather than an edit to be rediscovered.
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