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

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.

36 pages, 10 figures, 13 tables, 9 algorithms