标题： 非稀疏算子的自适应超简约：参数化粒子基动能等离子体模型的应用 显示英文标题

标题： Adaptive hyper-reduction of non-sparse operators: application to parametric particle-based kinetic plasma models

摘要： 本文提出了一种自适应超简约方法，以减少与参数化粒子基础动能等离子体模型模拟相关的计算成本，具体关注于Vlasov-Poisson方程。由于由粒子间相互作用产生的非线性算子的非稀疏性质，传统的模型降阶和超简约技术往往对此类模型无效。为了解决这一问题，我们提出了一个自适应的保结构超简约方法，该方法利用离散降维哈密顿量分解为少数状态分量的线性组合。所提出的近似策略允许：(i)保持问题的哈密顿结构；(ii)以计算高效的方式评估非线性非稀疏算子；(iii)通过逼近空间的演化和解的秩的自适应克服输运主导问题的Kolmogorov障碍。所提出的方法在数值基准模拟中得到验证，与全阶模型相比，表现出稳定且准确的性能，并且大幅减少了运行时间。 显示英文摘要

摘要： This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional model order reduction and hyper-reduction techniques are often ineffective for such models due to the non-sparse nature of the nonlinear operators arising from the interactions between particles. To tackle this issue, we propose an adaptive, structure-preserving hyper-reduction method that leverages a decomposition of the discrete reduced Hamiltonian into a linear combination of terms, each depending on a few components of the state. The proposed approximation strategy allows to: (i) preserve the Hamiltonian structure of the problem; (ii) evaluate nonlinear non-sparse operators in a computationally efficient way; (iii) overcome the Kolmogorov barrier of transport-dominated problems via evolution of the approximation space and adaptivity of the rank of the solution. The proposed method is validated on numerical benchmark simulations, demonstrating stable and accurate performance with substantial runtime reductions compared to the full order model.