Surrogate models for diffusion on graphs via sparse polynomials
This work addresses the gap in the literature for surrogate models for diffusion processes on graphs, which is significant for researchers and practitioners working with graph-based data.
This work tackles the problem of developing surrogate models for diffusion processes on graphs, resulting in sparse polynomial-based models with convergence guarantees. The models are demonstrated to be applicable on both synthetic and real-world graphs.
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.