Asikul Islam, Md Rezwan Bin Mizan, Maxim Olshanskii et al.
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.