Tensorial Reduced-Order Models for Parametric Coupled Reaction-Diffusion Systems: Application to Brain Tumor Growth Modeling

TL;DR

This paper develops tensor-based reduced-order models for efficient simulation of parametric reaction-diffusion systems, specifically applied to brain tumor growth, achieving significant speedups while maintaining accuracy.

Contribution

It introduces tensorial reduced-order models using Tucker and Tensor Train formats for coupled reaction-diffusion systems, improving computational efficiency over classical methods.

Findings

Achieved 85-120x speedup compared to full-order models.

Maintained high accuracy with up to 9 parameters.

Validated models on brain tumor growth simulations.

Abstract

We construct efficient surrogate models for parametric forward operators arising in brain tumor growth simulations, governed by coupled semilinear parabolic reaction-diffusion systems on heterogeneous two- and three-dimensional domains. We consider two models of increasing complexity: a scalar single-species formulation and a six-state, nine-parameter multi-species go-or-grow model. The governing equations are discretized using a finite volume method and integrated in time via an operator-splitting strategy. We develop tensorial reduced-order model (TROM) surrogates based on the Higher-Order Singular Value Decomposition in Tucker format and the Tensor Train decomposition, each in intrusive and non-intrusive variants. The models are compared against a classical proper orthogonal decomposition (POD) ROM baseline. Numerical experiments with up to $m=9$ model parameters demonstrate speedups of $85\times$-$120\times$ relative to the full-order solver while maintaining excellent accuracy, establishing tensorial surrogates as a rigorous and efficient computational foundation for many-query workflows.