# MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems

arXiv: https://arxiv.org/abs/2604.06881 · HTML: https://mlsanity.com/paper/2604.06881/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 30 of its 45 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [SinSR: Diffusion-Based Image Super-Resolution in a Single Step](https://mlsanity.com/paper/2311.14760/) (2023)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Inductive Moment Matching](https://mlsanity.com/paper/2503.07565/) (2025)
- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [Arbitrary-steps Image Super-resolution via Diffusion Inversion](https://mlsanity.com/paper/2412.09013/) (2024)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling](https://mlsanity.com/paper/2409.08477/) (2024)
- [Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems](https://mlsanity.com/paper/2503.13695/) (2025)
- [Blind Image Restoration via Fast Diffusion Inversion](https://mlsanity.com/paper/2405.19572/) (2024)
- [Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective](https://mlsanity.com/paper/2404.07200/) (2024)
- [Learning fast, accurate, and stable closures of a kinetic theory of an active fluid](https://mlsanity.com/paper/2308.06675/) (2023)
- [A scalable generative model for dynamical system reconstruction from neuroimaging data](https://mlsanity.com/paper/2411.02949/) (2024)
- [Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model](https://mlsanity.com/paper/2509.01293/) (2025)

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

- [Autoregressive One-Step Generative Modeling for Dynamical System Forecasting](https://mlsanity.com/paper/2605.05540/) (2026)
- [Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems](https://mlsanity.com/paper/2605.05975/) (2026)
- [Accelerating Redshift-Conditioned Galaxy Image Synthesis with One-step Generative Modeling](https://mlsanity.com/paper/2605.17546/) (2026)

## Abstract (arXiv)

Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, Fourier-based variants inherently truncate high-frequency components in spectral space, resulting in the loss of small-scale structures and degraded prediction quality at high resolutions when trained on low-resolution data. While diffusion-based enhancement methods can recover multi-scale features, they introduce substantial inference overhead that undermines the efficiency advantage of neural operators. In this work, we introduce MeanFlow-Enhanced Neural Operators (MENO), a novel framework that achieves accurate all-scale predictions with minimal inference cost. By leveraging the improved MeanFlow method, MENO restores both small-scale details and large-scale dynamics with superior physical fidelity and statistical accuracy. We evaluate MENO on three challenging dynamical systems, including phase-field dynamics, 2D Kolmogorov flow, and active matter dynamics, at resolutions up to 256×256. Across all benchmarks, MENO improves the power spectrum density accuracy by up to a factor of 2 compared to baseline neural operators while achieving up to 14× faster inference than the state-of-the-art Denoising Diffusion Implicit Model (DDIM)-enhanced counterparts, effectively bridging the gap between accuracy and efficiency. The flexibility and efficiency of MENO position it as an efficient surrogate model for scientific machine learning applications where both statistical integrity and computational efficiency are paramount.