An Agentic AI Scientific Community for Automated Neural Operator Discovery

We present an agentic approach to autonomous neural operator discovery based on an AI scientific community, which consists of a swarm of virtual laboratories that interact under a citation-based economy of influence. Highly-cited labs found new labs that follow their research direction and replace non-performing labs. Each virtual lab contains three agents: an LLM planner that writes a complete PyTorch program for a neural operator, a numerical worker that checks, repairs and trains it, and an LLM reviewer that participates in cross-lab peer review. The labs either compose neural operator building blocks (DeepONet/branch-trunk, Fourier, Transformer/attention, wavelet, and residual convolutional) in code, or write every layer from primitives. Simulation campaigns on the Darcy flow, Navier-Stokes and Allen-Cahn 2D problems show that the AI scientific community discovers operators that are more accurate than strong baselines on some problems, while no operator is the best on every problem. We also conduct comprehensive ablation studies to isolate the effects of using a community of labs versus a single lab, of allowing coding versus using a fixed vocabulary of blocks, and of using LLM agents versus rule-based alternatives, the latter on piecewise regression, the linear advection and Burgers 1D PDEs, and the Navier-Stokes and Darcy flow 2D PDEs. The code and full results are available at https://anonymous.4open.science/r/neural-operator-community.