GIT-Net：面向算子学习的广义积分变换
GIT-Net: Generalized Integral Transform for Operator Learning
AI总结：
本文提出 GIT-Net，利用深度神经网络参数化自适应广义积分变换来逼近 PDE 算子，在复杂几何问题上兼顾低测试误差与低计算开销，优于现有方法。
摘要：
本文介绍 GIT-Net，一种受积分变换算子启发、用于逼近偏微分方程（PDE）算子的深度神经网络架构。GIT-Net 利用了一个事实：常用于定义 PDE 的微分算子在特定函数基（如傅里叶基）中表达时，往往可以被简洁地表示。与刚性积分变换不同，GIT-Net 使用深度神经网络对自适应广义积分变换进行参数化。与近期提出的若干替代方法相比，GIT-Net 的计算和内存需求随网格离散化平滑扩展，便于将其应用于复杂几何上的 PDE 问题。数值实验表明，GIT-Net 是一种具有竞争力的神经网络算子，在一系列 PDE 问题上表现出较小的测试误差和较低的计算评估开销。这与现有神经网络算子形成对比，后者通常只在其中某一方面表现突出。
英文摘要：
This article introduces GIT-Net, a deep neural network architecture for approximating Partial Differential Equation (PDE) operators, inspired by integral transform operators. GIT-NET harnesses the fact that differential operators commonly used for defining PDEs can often be represented parsimoniously when expressed in specialized functional bases (e.g., Fourier basis). Unlike rigid integral transforms, GIT-Net parametrizes adaptive generalized integral transforms with deep neural networks. When compared to several recently proposed alternatives, GIT-Net's computational and memory requirements scale gracefully with mesh discretizations, facilitating its application to PDE problems on complex geometries. Numerical experiments demonstrate that GIT-Net is a competitive neural network operator, exhibiting small test errors and low evaluations across a range of PDE problems. This stands in contrast to existing neural network operators, which typically excel in just one of these areas.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
