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A dynamical variable-separation method FOR PARAMETER-DEPENDENT dynamical SYSTEMS

SIAM Journal on Scientific Computing 2025年第3期47卷 A1783-A1808页

作者： Chen, Liang Chen, Yaru Li, Qiuqi Zhou, Tao School of Mathematics Hunan University Changsha 410082 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper proposes a dynamical variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively enriching each term in the reduced basis functions via a greedy algorithm. This enables us to reformulate the problem to two decoupled evolution equations at each enrichment step, one of which is a parameter-independent PDE and the other a parameter-dependent ODE. These equations are directly derived from the original dynamical system and the previously separate representation terms. Moreover, the computational process of the proposed method can be split into an offline stage, in which the reduced basis functions are constructed, and an online stage, in which the efficient low-rank representation of the solution is employed. The proposed dynamical variable-separation method is capable of offering reduced computational complexity and enhanced efficiency compared to many existing low-rank separation techniques. Finally, we present various numerical results for linear/nonlinear parameter-dependent dynamical systems to demonstrate the effectiveness of the proposed method. © 2025 Society for Industrial and Applied Mathematics.

关键词： dynamical variable-separation method low-rank approximation model order reduction parameter-dependent dynamical systems

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