Framework of Multiple-point Statistical Simulation Using Manifold Learning for the Dimensionality Reduction of Patterns

Multiple-point statistics (MPS) has been successfully used for stochastic simulation by reproducing the features from training images (TIs) to the simulated regions. However, because these features mostly have intrinsic nonlinear relations, the MPS methods using linear dimensionality reduction are not suitable to handle nonlinear data. Since manifold learning methods can discover the intrinsic features of high-dimensional data by mapping them to a low-dimensional manifold, a framework using manifold learning for dimensionality reduction in MPS is proposed to resolve this issue, in which manifold learning methods are integrated with MPS to properly reduce the dimension of patterns from TIs so that the subsequent simulation can be more accurate. Besides, the proposed framework is designed for different situations of conditional data because of the great influence on simulation from conditional data. Tests are compared between manifold learning methods and linear method of dimensionality reduction, showing that compared with the typical linear dimension reduction method, the framework has obvious advantages in simulation quality.