1. Introduction
1.1. Surrogate modeling
1.2. Dimension reduction for high-dimensional UQ
1.3. Motivation and objectives of this study
2. Dimension reduction methods
2.1. Linear methods
2.2. Nonlinear spectral methods
2.3. Blind source separation methods
2.4. Non-convex methods
3. High-dimensional uncertainty quantification framework
3.1. Dimension reduction of high-dimensional inputs
3.2. Uncertainty propagation
3.3. Surrogate modeling via polynomial chaos expansion
3.4. Hyperparameter optimization
4. Numerical examples
5. Discussion