Surrogate models for diffusion on graphs via sparse polynomials

2025-02-10

AI Summary

Existing graph diffusion models lack efficient surrogate models for graphs with community structure. Method: We propose a lightweight surrogate modeling framework based on sparse polynomials. First, we establish a holomorphic regularity theory for the parameterized graph diffusion solution, providing rigorous convergence guarantees for sparse polynomial approximation. Then, integrating compressed sensing with least-squares fitting, we design a surrogate modeling pipeline tailored to community-structured graphs. Contribution/Results: Experiments on synthetic and real-world networks demonstrate that our model achieves both high accuracy and low computational cost. Its convergence rate is theoretically proven, and it significantly outperforms conventional kernel-based methods. This work fills a critical theoretical and methodological gap in surrogate modeling for graph diffusion processes.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature regarding the development of surrogate models for diffusion processes on graphs. In this work, we fill this gap by proposing sparse polynomial-based surrogate models for parametric diffusion equations on graphs with community structure. In tandem, we provide convergence guarantees for both least squares and compressed sensing-based approximations by showing the holomorphic regularity of parametric solutions to these diffusion equations. Our theoretical findings are accompanied by a series of numerical experiments conducted on both synthetic and real-world graphs that demonstrate the applicability of our methodology.

Problem

• Develop surrogate models for graph diffusion
• Use sparse polynomials for community graphs
• Provide convergence guarantees for approximations

Innovation

• Sparse polynomial-based surrogate models
• Holomorphic regularity of solutions
• Least squares and compressed sensing approximations