# Surrogate models for diffusion on graphs via sparse polynomials

arXiv: https://arxiv.org/abs/2502.06595 · HTML: https://mlsanity.com/paper/2502.06595/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 65 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator](https://mlsanity.com/paper/1801.10108/) (2018)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Lipschitz regularity of graph Laplacians on random data clouds](https://mlsanity.com/paper/2007.06679/) (2020)
- [Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data](https://mlsanity.com/paper/2012.06081/) (2020)
- [Fluid Communities: A Competitive, Scalable and Diverse Community Detection Algorithm](https://mlsanity.com/paper/1703.09307/) (2017)

## Built on by (most cited first, 1 of 1)

- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)

## Abstract (arXiv)

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.