MENO让神经算子在保持高效的同时,精准预测动态系统的多尺度细节。
MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems

- 用改进的均流机制恢复高频细节和大尺度动态,无需复杂扩散过程。
- 在256×256分辨率下,功率谱精度提升最高达2倍,推理速度比DDIM增强版快14倍。
- 适合需要高保真度与低延迟的科学机器学习场景,如流体模拟、相场演化。
神经算子因其网格无关性和计算效率,已成为动态系统的重要代理模型。然而,基于傅里叶的方法在频域会截断高频成分,导致在低分辨率数据上训练时,高分辨率下小尺度结构丢失,预测质量下降。尽管扩散增强方法可恢复多尺度特征,但引入了显著的推理开销,削弱了神经算子的效率优势。本文提出均流增强型神经算子(MENO),在极低推理成本下实现全尺度精确预测。通过改进的均流方法,MENO同时恢复小尺度细节与大尺度动力学,具备更优的物理保真度与统计精度。我们在三类挑战性动态系统——相场动力学、二维柯尔莫戈洛夫流和活性物质动力学——上进行评估,最高分辨率达256×256。所有基准测试中,MENO的功率谱密度精度相比基线提升最高达2倍,且推理速度比当前最优的去噪扩散隐式模型(DDIM)增强版本快至14倍,有效弥合了精度与效率的鸿沟。MENO的灵活性与高效性使其成为科学机器学习中兼顾统计完整性和计算效率的理想替代方案。
原文摘要 · Abstract (English)
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$\times$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 $14\times$ 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.
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