[论文] Inertial Manifold Neural Operator for Dissipative Time-Dependent Parti...

论文概要

研究领域: ML
作者: Xiaoyang Xie, Clarence W. Rowley
发布时间: 2025-08-26
arXiv: 2508.17622

中文摘要

本文提出了惯性流形神经算子（IMNO），用于求解耗散型时间依赖偏微分方程（PDE）。这类系统的长时间动力学由于耗散效应往往表现出有效的低维结构。与标准的神经算子架构（如傅里叶神经算子FNO）不同，IMNO显式利用这种低维结构，在非线性耗散PDE的长程自回归训练和预测中实现更好的物理解释性、精度和稳定性。对于平移等变PDE，我们进一步提出了平移等变变体IMNO-SE，确保输入的空间平移在输出中诱导相同的空间平移。这种保持对称性的归纳偏置显著提升了其在平移等变PDE中的性能。

原文摘要

In this paper, we introduce the Inertial Manifold Neural Operator (IMNO) for solving dissipative time-dependent partial differential equations (PDEs). The long-time dynamics of such systems often exhibit an effective low-dimensional structure due to dissipation. Unlike standard neural operator architectures such as the Fourier Neural Operator (FNO), IMNO explicitly leverages the low-dimensional structure to achieve better physical interpretability, accuracy, and stability in long-horizon autoregressive training and prediction for nonlinear dissipative PDEs. For shift-equivariant PDEs, we further introduce a shift-equivariant variant (IMNO-SE) of the proposed neural operator, ensuring that a spatial shift in the input induces the same spatial shift in the output. This symmetry-preserving in...

自动采集于 2026-08-26

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