Proficient Graph Neural Network Design by Accumulating Knowledge on Large Language Models

High-level automation is increasingly critical in AI, driven by rapid advances in large language models (LLMs) and AI agents. However, LLMs, despite their general reasoning power, struggle significantly in specialized, data-sensitive tasks such as designing Graph Neural Networks (GNNs). This difficulty arises from (1) the inherent knowledge gaps in modeling the intricate, varying relationships between graph properties and suitable architectures and (2) the external noise from misleading descriptive inputs, often resulting in generic or even misleading model suggestions. Achieving proficiency in designing data-aware models -- defined as the meta-level capability to systematically accumulate, interpret, and apply data-specific design knowledge -- remains challenging for existing automated approaches, due to their inefficient construction and application of meta-knowledge. To achieve the meta-level proficiency, we propose DesiGNN, a knowledge-centered framework that systematically converts past model design experiences into structured, fine-grained knowledge priors well fitted to meta-learning with LLMs. To account for the inherent variability and external noise, DesiGNN aligns empirical property filtering from extensive benchmarks with adaptive elicitation of literature insights via LLMs. By constructing a solid meta-knowledge between unseen graph understanding and known effective architecture patterns, DesiGNN can deliver top-5.77% initial model proposals for unseen datasets within seconds, and achieve consistently superior performance with minimal search costs against baselines.