用对数方法高效计算高维系统的动力学生成器，避免时间微分。
Tensor-based computation of the Koopman generator via operator logarithm
- 通过奇异值分解的对数运算，在张量列车格式中求解科普曼生成器。
- 在4维洛特卡-沃尔泰拉和10维洛伦兹-96系统中准确恢复系数，支持高维扩展。
- 适合研究高维非线性动力系统建模与数据驱动分析的科研人员。
从数据中识别非线性动力系统的控制方程极具挑战性。尽管稀疏非线性动力学识别（SINDy）及其扩展方法广泛应用，但基于算子对数的方法通过避免时间微分，可支持更大采样间隔。然而，这些方法仍受维度诅咒困扰。本文提出一种数据驱动方法，通过取科普曼特征值的对数，将科普曼生成器以低秩张量列车（TT）格式计算并保持其结构。在4维洛特卡-沃尔泰拉和10维洛伦兹-96系统上的实验表明，该方法能准确恢复向量场系数，并具备向更高维系统扩展的潜力。
原文摘要 · Abstract (English)
Identifying governing equations of nonlinear dynamical systems from data is challenging. While sparse identification of nonlinear dynamics (SINDy) and its extensions are widely used for system identification, operator-logarithm approaches use the logarithm to avoid time differentiation, enabling larger sampling intervals. However, they still suffer from the curse of dimensionality. Then, we propose a data-driven method to compute the Koopman generator in a low-rank tensor train (TT) format by taking logarithms of Koopman eigenvalues while preserving the TT format. Experiments on 4-dimensional Lotka-Volterra and 10-dimensional Lorenz-96 systems show accurate recovery of vector field coefficients and scalability to higher-dimensional systems.
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