The primary objective of this study is to remove duplicated monomial contributions that proliferate in Carleman linearization as state dimension and truncation order increase. To do so, we adopt a shift-and-lift architecture, since it exposes repeated exponent targets and allows duplicate-aware coefficient coalescing during lifted-operator assembly. This architecture also makes high-order truncation practical, but that regime intensifies local convergence and closure sensitivity for higher-order nonlinearities. We therefore pair shift-and-lift with a moving-center expansion so that shift and lift are updated jointly around evolving local centers, improving validity of the truncated model along the trajectory. The resulting workflow combines symmetry-reduced monomial bases, packed exponent-key indexing, and sparse triplet coalescing to preserve truncated affine dynamics while reducing index-resolution overhead and write-path irregularity. We analyze variable growth, preprocessing complexity, and truncation-induced error mechanisms, and we compare against Jacobian linearization through fixed-step error, admissible step size, and cost-at-target-accuracy criteria. Two benchmarks (bilinear driver and logistic interaction) show convergence under refinement for both approaches, with regime-dependent accuracy gains for the proposed method rather than universal superiority.

翻译：本研究的主要目标是消除卡莱曼线性化中随状态维度和截断阶数增加而激增的重复单项贡献。为此，我们采用移位-提升架构，该架构能暴露重复的指数目标，并允许在提升算子组装过程中实现重复感知的系数合并。该架构还使高阶截断变得可行，但这种模式会加剧高阶非线性的局部收敛与闭包敏感性。因此，我们将移位-提升与移动中心展开相结合，使移位和提升围绕演化的局部中心联合更新，从而提高截断模型沿轨迹的有效性。所得工作流程整合了对称约化的单项基、压缩指数键索引与稀疏三元组合并，在保留截断仿射动力学的同时降低了索引解析开销与写入路径不规则性。我们分析了变量增长、预处理复杂度与截断引发的误差机制，并通过固定步长误差、容许步长及目标精度成本准则与雅可比线性化进行了对比。两个基准测试（双线性驱动与逻辑交互）表明，两种方法在细化过程中均能收敛，而所提方法在特定场景下具有精度优势，并非普遍优越。