Model reduction in Smoluchowski-type equations

TL;DR

This paper applies Proper Orthogonal Decomposition to reduce the complexity of Smoluchowski aggregation equations, enabling efficient approximation and reconstruction of solutions with lower computational costs.

Contribution

It introduces a POD-based model reduction approach for Smoluchowski equations and a method for reconstructing the reduced space without full problem solutions.

Findings

Existence of a low-dimensional space for solution approximation

Model complexity depends only on the reduced space dimension

Reconstruction method accelerates computations significantly

Abstract

In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a low-dimensional space allowing to approximate the solutions of aggregation equations. We also demonstrate that it is possible to model the aggregation process with the complexity depending only on dimension of such a space but not on the original problem size. In addition, we propose a method for reconstruction of the necessary space without solving of the full evolutionary problem, which can lead to significant acceleration of computations, examples of which are also presented.