This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD), a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both spatiotemporal and purely temporal data. By incorporating time-delay embedding and leveraging Orthogonal Matching Pursuit (OMP), parsDMD ensures robustness against noise and effectively handles complex, nonlinear dynamics. The algorithm is validated on a diverse range of datasets, including standing wave signals, identifying hidden dynamics, fluid dynamics simulations (flow past a cylinder and transonic buffet), and atmospheric sea-surface temperature (SST) data. ParsDMD addresses a significant limitation of the traditional sparsity-promoting DMD (spDMD), which requires manual tuning of sparsity parameters through a rigorous trial-and-error process to balance between single-mode and all-mode solutions. In contrast, parsDMD autonomously determines the optimally sparse subset of modes without user intervention, while maintaining minimal computational complexity. Comparative analyses demonstrate that parsDMD consistently outperforms spDMD by providing more accurate mode identification and effective reconstruction in noisy environments. These advantages render parsDMD an effective tool for real-time diagnostics, forecasting, and reduced-order model construction across various disciplines.

翻译：本文提出简约动态模态分解（parsDMD）算法，该算法能够自动为时空数据及纯时序数据选择最优稀疏动态模态子集。通过结合时滞嵌入技术并利用正交匹配追踪（OMP）方法，parsDMD在噪声环境下具有鲁棒性，并能有效处理复杂的非线性动态系统。该算法在多种数据集上得到验证，包括驻波信号识别、隐藏动态特征提取、流体动力学模拟（圆柱绕流与跨声速抖振）以及海表温度（SST）大气数据。parsDMD解决了传统稀疏促进动态模态分解（spDMD）的重要缺陷——后者需要通过严格的试错过程手动调整稀疏参数以平衡单模态解与全模态解。相比之下，parsDMD能够在无需人工干预的情况下自主确定最优稀疏模态子集，同时保持最低计算复杂度。对比分析表明，parsDMD在噪声环境中始终优于spDMD，能提供更精确的模态识别与更有效的信号重构。这些优势使得parsDMD成为跨学科实时诊断、预测与降阶模型构建的有效工具。