非线性动力系统多维近似
Multidimensional approximation of nonlinear dynamical systems
AI总结：
本文提出MANDy方法，通过结合数据驱动方法与张量网络分解，解决高维非线性动力系统建模中的维度灾难问题，提高计算效率和存储效率。
摘要：
在非线性动力系统建模和分析领域，从测量数据中恢复未知控制方程是一个关键任务。这种重要的系统识别实例在工业工程、声学信号处理和股票市场模型等应用领域中都有广泛的应用。为了找到合适的底层动力系统表示，不同社区已经提出了各种数据驱动方法。然而，如果给定的数据集是高维的，这些方法通常会受到维度灾难的影响。为了显著减少计算成本和存储消耗，我们提出了一种结合数据驱动方法与张量网络分解的MANDy方法。通过几种高维非线性动力系统，将介绍所提出方法的效率。
英文摘要：
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method MANDy which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
