张量降阶模型用于参数耦合反应扩散系统的建模：应用于脑肿瘤生长建模
Tensorial Reduced-Order Models for Parametric Coupled Reaction-Diffusion Systems: Application to Brain Tumor Growth Modeling
AI总结：
本文提出张量降阶模型用于参数化前向算子的高效代理模型，应用于脑肿瘤生长模拟，通过比较经典POD ROM基线，展示了张量代理模型在多查询工作流中的高效性和准确性。
摘要：
我们构建了用于脑肿瘤生长模拟的高效代理模型，这些模型由耦合的半线性抛物型反应扩散系统在异质二维和三维域上 governed。我们考虑了两种复杂度递增的模型：单物种标量模型和六状态、九参数多物种go-or-grow模型。 governing方程使用有限体积法离散化，并通过操作符分裂策略进行时间积分。我们开发了基于Tucker格式的高阶奇异值分解和张量列车分解的张量降阶模型（TROM）代理模型，分别采用侵入式和非侵入式变体。模型与经典POD ROM基线进行比较。具有多达m=9个模型参数的数值实验表明，相对于全阶求解器，速度提升了85×-120×，同时保持了出色的准确性，证明了张量代理模型作为多查询工作流的严格且高效的计算基础。
英文摘要：
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.
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