Polynomial Chaos Expansion

Polynomial Chaos Expansion (PCE) is a powerful technique for representing the uncertainty in the output of a system with uncertain inputs, primarily aiming to create efficient surrogate models for computationally expensive simulations. Current research focuses on improving PCE's accuracy and efficiency through sparse approximations, incorporating physical constraints, and integrating it with other methods like Bayesian optimization, Gaussian processes, deep neural networks, and manifold learning to handle high-dimensionality and non-linearity. This allows for more accurate uncertainty quantification and sensitivity analysis in various fields, including engineering, finance, and scientific computing, ultimately reducing the computational cost of complex simulations and improving decision-making under uncertainty.