# NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

arXiv: https://arxiv.org/abs/2602.22059 · HTML: https://mlsanity.com/paper/2602.22059/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 24 of 24)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (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)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Multiple Physics Pretraining for Physical Surrogate Models](https://mlsanity.com/paper/2310.02994/) (2023)
- [CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics](https://mlsanity.com/paper/2310.05963/) (2023)
- [Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers](https://mlsanity.com/paper/2405.17527/) (2024)
- [ViTO: Vision Transformer-Operator](https://mlsanity.com/paper/2303.08891/) (2023)
- [HMoE: Heterogeneous Mixture of Experts for Language Modeling](https://mlsanity.com/paper/2408.10681/) (2024)
- [Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2510.25803/) (2025)

## Built on by (most cited first, 3 of 3)

- [Temperature Field Reconstruction of Tungsten Monoblock Divertor on EAST using Physics-aware Neural Operator Transformer](https://mlsanity.com/paper/2606.31574/) (2026)
- [SPEAR: A Spectral-Disentangled MoE Neural Operator with Knowledge-Guided Expert Aggregation for Large-Scale PDE Pretraining](https://mlsanity.com/paper/2610.03265/) (2026)
- [COSMOS: Soft Mechanism Mixtures with Verifiable Routing for Long-Horizon PDE Forecasting](https://mlsanity.com/paper/2610.04427/) (2026)

## Abstract (arXiv)

Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE systems, existing neural operators typically rely on a single network architecture, which limits their capacity to fully capture heterogeneous features and complex system dependencies. This constraint poses a bottleneck for large-scale PDE pre-training based on neural operators. To address these challenges, we propose a large-scale PDE pre-trained neural operator based on a nested Mixture-of-Experts (MoE) framework. In particular, the image-level MoE is designed to capture global dependencies, while the token-level Sub-MoE focuses on local dependencies. Our model can selectively activate the most suitable expert networks for a given input, thereby enhancing generalization and transferability. We conduct large-scale pre-training on twelve PDE datasets from diverse sources and successfully transfer the model to downstream tasks. Extensive experiments demonstrate the effectiveness of our approach.