# An Agentic AI Scientific Community for Automated Neural Operator Discovery

arXiv: https://arxiv.org/abs/2607.12122 · HTML: https://mlsanity.com/paper/2607.12122/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 21 of its 27 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 21 of 21)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Towards End-to-End Automation of AI Research](https://mlsanity.com/paper/2606.15497/) (2026)
- [AutoML-Zero: Evolving Machine Learning Algorithms From Scratch](https://mlsanity.com/paper/2003.03384/) (2020)
- [EvoPrompting: Language Models for Code-Level Neural Architecture Search](https://mlsanity.com/paper/2302.14838/) (2023)
- [Can GPT-4 Perform Neural Architecture Search?](https://mlsanity.com/paper/2304.10970/) (2023)
- [SCORES: Shape Composition with Recursive Substructure Priors](https://mlsanity.com/paper/1809.05398/) (2018)
- [ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2512.03476/) (2025)
- [The AI Scientific Community: Agentic Virtual Lab Swarms](https://mlsanity.com/paper/2603.21344/) (2026)

## Built on by (most cited first, 2 of 2)

- [SwarmWorld: Stigmergic technological evolution in societies of language-model agents](https://mlsanity.com/paper/2608.26081/) (2026)
- [LLM-IDEA: Identifiability-Driven Experimental Agent for Autonomous Discovery of Mechanistic World Models](https://mlsanity.com/paper/2610.11253/) (2026)

## Abstract (arXiv)

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 proposes an architecture, a numerical worker that trains and measures it, and an LLM reviewer that participates in cross-lab peer review. All labs share a common vocabulary consisting of DeepONet (branch-trunk), Fourier, Transformer (attention), wavelet, and residual convolutional neural operator building blocks. We evaluate the neural operator AI scientific community on five problems, namely piecewise regression, the linear advection and Burgers 1D PDEs, and the Navier-Stokes and Darcy flow 2D PDEs, while repeating the simulation three times for each problem. The results show that the neural operator AI scientific community is capable of discovering high-accuracy, low-parameter-count neural operator architectures. All 9,623 LLM calls are logged and audited, which reveals that the virtual lab LLM planners choose to hybridize in 99.8% of their logged decisions, consistently returning multi-family hybrids. Moreover, we conducted an ablation study by replacing the LLM agents in each lab by rule-based alternatives, which caused the scientific community to collapse to non-hybridized single-family stacks in several cases, showing that LLM agency is needed to preserve diversity. The results suggest a no-free-lunch theorem for neural operators: there is no universal winner. The code, configurations, and the complete LLM transcripts are released at https://github.com/luislootx/AI-SC.