AI Community Discovers Neural Operators Autonomously.

A novel approach to automated scientific discovery involves an "AI scientific community" designed to find new neural operator architectures. This community consists of numerous virtual laboratories, each equipped with an LLM planner to propose architectures, a numerical worker to train and evaluate them, and an LLM reviewer for peer assessment. These labs interact within a citation-based economy, where successful labs influence the creation of new ones and underperforming labs are replaced. The virtual labs share a common set of neural operator building blocks, including DeepONet, Fourier, Transformer, wavelet, and residual convolutional components. The system was tested on five different problems, ranging from piecewise regression to complex PDEs like Navier-Stokes and Darcy flow. The results consistently showed that this AI community could discover neural operator architectures that achieve high accuracy with a low number of parameters. Analysis of over 9,000 LLM calls revealed that the LLM planners predominantly chose to hybridize different building blocks, demonstrating a preference for multi-family solutions. An ablation study confirmed the importance of LLM agency, as replacing LLM agents with rule-based alternatives led to a collapse in architectural diversity. This suggests that a "no-free-lunch" theorem applies to neural operators, implying no single universal winner, and highlights the potential of agentic AI for complex scientific exploration.