arXiv:2509.24868cs.LGphysics.comp-ph2025-09中稿 · ICLR被引 1

用谱域与图像域双分支设计,提升偏微分方程求解的全局一致性与稳定性。

DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learning

  • 双分支结构分离处理低频全局信息与高频局部细节
  • 带权融合机制减少参数量,降低误差累积,提升推理速度
  • 在纳维-斯托克斯方程上实现7%~54%误差下降,适合高精度仿真场景

与传统数值求解器相比,神经求解器在学习偏微分方程(PDE)动力学时可显著提升运行效率与精度。近年来,基于多尺度窗口自注意力的模型广泛采用,如Poseidon中的scOT骨干网络。然而,由于其局部性,全局谱耦合需通过深层堆叠和窗口移动逐步传播,导致耦合弱化、闭环推演中误差积累与漂移。为此,本文提出DRIFT-Net,采用谱分支与图像分支双路径设计:谱分支捕捉全局低频信息,图像分支聚焦局部细节与非平稳结构。首先在低频范围内进行轻量级可控混合,再通过带权重方式在每层融合两路径输出,避免简单拼接带来的宽度膨胀与训练不稳。融合结果转换回空间域后叠加至图像分支,实现跨尺度的全局结构保持与高频细节保留。相比强基准模型,在相同训练设置与预算下,DRIFT-Net实现更低误差、更高吞吐率且参数量减少约15%。在纳维-斯托克斯基准测试中,相对$L_1$误差降低7%–54%,吞吐优于scOT。消融实验与理论分析验证了该设计的稳定性和有效性。代码已开源:https://github.com/cruiseresearchgroup/DRIFT-Net。

原文摘要 · Abstract (English)

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative $L_{1}$ error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

偏微分方程神经算子谱方法高效建模

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