Reconstruction of diffusions using spectral data from timeseries
Reconstruction of diffusions using spectral data from timeseries
复制标题
使用时间序列的光谱数据重建扩散
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
E. Vanden
中科院分区：
文献类型：
--
作者：
D. Crommelin;E. Vanden
抽象的。提出了一种从数据重建扩散过程（简称扩散）的数值方法。通过最小化一个目标函数，该目标函数测量算子的本征谱和参考本征谱之间的差异，发现扩散的生成器的漂移和扩散系数。参考光谱可以通过构建离散时间马尔可夫链从时间序列中以离散形式获得。福克-普朗克算子的离散化将目标函数的最小化转化为凸域上的二次规划问题，对于该凸域，存在完善的求解方法。该技术是一个推广的连续时间马尔可夫链发生器，最近开发的重建过程。该技术还允许导出多时间尺度系统中慢变量的均匀化扩散系数。
Abstract. A numerical technique for the reconstruction of diffusion processes (diffusions, in short) from data is presented. The drift and diffusion coefficients of the generator of the diffusion are found by minimizing an object function which measures the difference between the eigenspectrum of the operator and a reference eigenspectrum. The reference spectrum can be obtained, in discretized form, from timeseries through the construction of a discrete-time Markov chain. Discretization of the Fokker-Planck operator turns minimization of the object function into a quadratic programming problem on a convex domain, for which well-established solution methods exist. The technique is a generalization of a reconstruction procedure for continuous-time Markov chain generators, recently developed by the authors. The technique also allows to derive the coefficient in the homogenized diffusion for the slow variables in system with multiple timescales.