Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery

Hugging Face Daily Papers Papers
ai-agents scientific-computing numerical-solvers self-improvement code-generation scientific-ml

Summary

The paper introduces Auto-Diagnosis and Skill Discovery (ADSD), a framework that teaches AI agents to diagnose why numerical solvers perform poorly and then discover reusable solver skills, achieving up to 71x error reduction on power flow benchmarks and transferring to unseen grid topologies.

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.
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Paper page - Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery

Source: https://huggingface.co/papers/2610.03872

Abstract

AIagentsarebecomingincreasinglycapableofgeneratingscientificcode,butgeneratingcodeisnotthesameasimprovingthealgorithmsbehindit.Fornumericalsolvers,executionfeedbackcanexposepoorperformance,butrarelyrevealsitsunderlyingcauseandhowtoaddressit.WeintroduceAuto-DiagnosisandSkillDiscovery(ADSD),aframeworkthatlinksnumericaldiagnosistoreusablesolverself-improvement.ADSDfollowsadiagnosis-firstparadigmthatfirstexplainswhyasolverperformspoorly,thenusesthisdiagnosistoguidethediscoveryofappropriatenumericalmethods.Theresultingknowledgeispackagedintoreusablesolverskills,turningsolverimprovementfromtrial-and-erroreditingintoastructuredprocessofdiagnosis,discovery,andimplementation.Acrossfourchallengingnumericaldomains--powerflowequation,ACoptimalpowerflowcontrol,stiffordinarydifferentialequations,andheterogeneousdiffusionPDEs--ADSDconsistentlyimprovessolveraccuracy,robustness,andefficiency.OnGOC-500powerflow,forexample,ADSDreducesmeansolvererrorbynearly71times,withimprovementsfurthertransferringtounseengridtopologiesandoperatingregimes.

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