A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction.
Sijing LiZhiwen ZhangHongkai ZhaoPublished in: CoRR (2019)
Keyphrases
- dimension reduction
- partial differential equations
- multiscale
- wavelet coefficients
- intrinsic dimension
- image denoising
- image processing
- principal component analysis
- feature extraction
- wavelet transform
- low dimensional
- high dimensional problems
- high dimensional
- high dimensional data
- singular value decomposition
- partial least squares
- random projections
- numerical solution
- level set
- variable selection
- linear discriminant analysis
- manifold learning
- feature selection
- high dimensionality
- sparse metric learning
- cluster analysis
- natural images
- dimensionality reduction
- feature space
- image representation
- shape representation
- high dimensional data analysis
- differential equations
- preprocessing
- discriminative information
- image segmentation
- computer vision
- real world
- dimension reduction methods
- manifold embedding
- feature vectors
- nearest neighbor
- maximum likelihood
- unsupervised learning