具有尺度感知神经恢复的多级图小波压缩感知

中文摘要 AI 辅助

科学机器学习方法如神经算子和物理信息神经网络推动了工程应用和反问题发展，但训练通常需大量模拟数据，导致数据准备和模型训练成本高昂。我们提出图小波压缩感知（GWCS），这是一种基于学习的框架，用于通过谱图小波变换将图信号表示为稀疏、可解释的小波域表示，从而对图信号进行离线压缩。该框架结合了非参数多级重要性采样器（在给定压缩率下在每个尺度内保留高能小波系数）和从稀疏系数重建信号的尺度感知图神经网络。我们在随机图上的合成近似带限图信号以及四个网格上的偏微分方程模拟数据集（包括湍流辐射层、粘弹性不稳定性、柯尔莫哥洛夫流和动态失速）上评估了所提出的框架，并与图信号采样方法和图自动编码器基线进行了比较。结果表明，与现有基准相比，该框架实现了高重建保真度和显著的数据压缩。

英文摘要

Scientific machine learning methods such as neural operators and physics-informed neural networks have advanced engineering applications and inverse problems, but their training typically requires large volumes of simulated data. This makes data preparation and model training expensive. We propose Graph Wavelet Compressed Sensing (GWCS), a learning-based framework for offline compression of graph signals by representing them as sparse, interpretable wavelet-domain representations using the spectral graph wavelet transform. The framework combines a nonparametric multilevel importance sampler, which retains high-energy wavelet coefficients within each scale for a given compression ratio, with a scale-aware graph neural network that reconstructs the signal from the sparse coefficients. We evaluate the proposed framework on synthetic approximately band-limited graph signals over random graphs and four PDE simulation datasets over meshes, which include Turbulent Radiative Layer, Viscoelastic Instability, Kolmogorov Flow, and Dynamic Stall. We compare against graph signal sampling methods and graph autoencoder baselines. Results demonstrate that the framework achieves high reconstruction fidelity and substantial data compression compared to existing benchmarks.

发表机构

• Simplicial Technologies Inc.（单纯技术公司）
• New Jersey Institute of Technology（新泽西理工学院）
• Brown University（布朗大学）
• Siemens Foundational Technology（西门子基础技术公司）

机构由 AI 辅助整理，请以论文原文为准。