Nonintrusive model order reduction for cross-diffusion systems

TL;DR

This paper develops tensor-based nonintrusive reduced-order models for parametric cross-diffusion systems, achieving significant computational savings while accurately predicting complex spatiotemporal patterns.

Contribution

It introduces a novel two-level tensor approach using HOSVD and RBF interpolation for efficient nonintrusive ROMs of cross-diffusion equations.

Findings

Achieves 2-3x speed-up over full models

Accurately predicts complex spatiotemporal patterns

Demonstrates effectiveness on 2D and 3D systems

Abstract

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting from finite-difference discretization of the differential operators by taking the advantage of Kronecker structure. The matrix/tensor differential equations are integrated in time with the implicit-explicit (IMEX) Euler method. The reduced bases, relying on a finite sample set of parameter values, are constructed in form of a two-level approach by applying higher-order singular value decomposition (HOSVD) to the space-time snapshots in tensor form, which leads to a large amount of computational and memory savings. The nonintrusive reduced approximations for an arbitrary parameter value are obtained through tensor product of the reduced basis by the parameter dependent core tensor that contains the reduced coefficients. The reduced coefficients for new parameter values are computed using radial basis function (RBF) interpolation. The efficiency of the proposed method is illustrated through numerical experiments for two-dimensional Schnakenberg and three-dimensional Brusselator cross-diffusion equations. The spatiotemporal patterns are accurately predicted by the reduced-order models with speed-up factors of orders two and three over the full-order models.