轻量级神经算子D-SENO加速求解多类微分方程,训练快20倍且精度不降。
Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations
- 融合空洞卷积与通道注意力,兼顾大范围依赖与动态特征重校准。
- 在多个物理方程上实现约20倍训练加速,精度优于或匹配主流模型。
- 适合需快速模拟的工程场景,如空气动力学与多孔介质流体建模。
快速准确的物理驱动偏微分方程(PDE)代理模型在空气动力学、多孔介质设计和流动控制等领域至关重要。然而,许多基于Transformer的模型和现有神经算子参数量庞大,导致训练成本高、部署缓慢。本文提出D-SENO(空洞挤压-激励神经算子),一种轻量级算子学习框架,可高效求解多种PDE,包括机翼势流、多孔介质中的达西流、管道泊肃叶流及不可压缩纳维-斯托克斯涡流场。D-SENO结合空洞卷积(DC)块与挤压-激励(SE)模块,联合捕捉宽感受野与动态特性,同时实现通道注意力。精心选择的空洞率使感受野聚焦关键区域,有效建模长程物理依赖;而SE模块则自适应重校准特征通道,突出动态相关尺度。模型训练速度比标准Transformer模型快约20倍,且在多个PDE基准测试中精度优于或匹配现有方法。消融实验表明,移除SE模块会导致性能轻微下降。
原文摘要 · Abstract (English)
Fast and accurate surrogates for physics-driven partial differential equations (PDEs) are essential in fields such as aerodynamics, porous media design, and flow control. However, many transformer-based models and existing neural operators remain parameter-heavy, resulting in costly training and sluggish deployment. We propose D-SENO (Dilated Squeeze-Excitation Neural Operator), a lightweight operator learning framework for efficiently solving a wide range of PDEs, including airfoil potential flow, Darcy flow in porous media, pipe Poiseuille flow, and incompressible Navier Stokes vortical fields. D-SENO combines dilated convolution (DC) blocks with squeeze-and-excitation (SE) modules to jointly capture wide receptive fields and dynamics alongside channel-wise attention, enabling both accurate and efficient PDE inference. Carefully chosen dilation rates allow the receptive field to focus on critical regions, effectively modeling long-range physical dependencies. Meanwhile, the SE modules adaptively recalibrate feature channels to emphasize dynamically relevant scales. Our model achieves training speed of up to approximately $20\times$ faster than standard transformer-based models and neural operators, while also surpassing (or matching) them in accuracy across multiple PDE benchmarks. Ablation studies show that removing the SE modules leads to a slight drop in performance.
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