Multilevel Graph Wavelet Compressed Sensing with Scale-Aware Neural Recovery

2026-07-22

AI Summary

This work addresses the high training cost of scientific machine learning due to its reliance on large-scale simulation data by proposing a Graph Wavelet Compressive Sensing (GWCS) framework. The method leverages spectral graph wavelet transforms to compress graph signals into sparse, interpretable representations in the wavelet domain and integrates multi-level importance sampling with a scale-aware graph neural network for efficient signal reconstruction. By significantly reducing data requirements while preserving high-fidelity reconstructions, GWCS outperforms existing graph signal sampling approaches and graph autoencoder baselines across both synthetic graph signals and four benchmark datasets derived from partial differential equation simulations, achieving superior compression ratios and reconstruction accuracy.

Abstract

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.

Problem

• scientific machine learning
• data compression
• graph signals
• inverse problems
• training cost

Innovation

• Graph Wavelet Compressed Sensing
• Scale-Aware Neural Recovery
• Spectral Graph Wavelet Transform
• Multilevel Importance Sampling
• Graph Neural Networks