# From Uniform to Adaptive: General Skip-Block Mechanisms for Efficient PDE Neural Operators

arXiv: https://arxiv.org/abs/2511.00032 · HTML: https://mlsanity.com/paper/2511.00032/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [DynamicViT: Efficient Vision Transformers with Dynamic Token Sparsification](https://mlsanity.com/paper/2106.02034/) (2021)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [Evaluating Layers of Representation in Neural Machine Translation on Part-of-Speech and Semantic Tagging Tasks](https://mlsanity.com/paper/1801.07772/) (2018)
- [Inducing Point Operator Transformer: A Flexible and Scalable Architecture for Solving PDEs](https://mlsanity.com/paper/2312.10975/) (2023)

## Abstract (arXiv)

In recent years, Neural Operators(NO) have gradually emerged as a popular approach for solving Partial Differential Equations (PDEs). However, their application to large-scale engineering tasks suffers from significant computational overhead. And the fact that current models impose a uniform computational cost while physical fields exhibit vastly different complexities constitutes a fundamental mismatch, which is the root of this inefficiency. For instance, in turbulence flows, intricate vortex regions require deeper network processing compared to stable flows. To address this, we introduce a framework: Skip-Block Routing (SBR), a general framework designed for Transformer-based neural operators, capable of being integrated into their multi-layer architectures. First, SBR uses a routing mechanism to learn the complexity and ranking of tokens, which is then applied during inference. Then, in later layers, it decides how many tokens are passed forward based on this ranking. This way, the model focuses more processing capacity on the tokens that are more complex. Experiments demonstrate that SBR is a general framework that seamlessly integrates into various neural operators. Our method reduces computational cost by approximately 50% in terms of Floating Point Operations (FLOPs), while still delivering up to 2x faster inference without sacrificing accuracy.