Polynomial Chaos

Polynomial chaos (PC) is a powerful technique for representing and analyzing systems with inherent uncertainties, primarily by approximating functions of random variables using orthogonal polynomials. Current research focuses on enhancing PC's accuracy and efficiency, particularly through hybrid approaches combining PC with machine learning methods like Gaussian processes and deep neural networks, leading to improved surrogate models for complex systems. These advancements enable more accurate and computationally efficient uncertainty quantification and reliability analysis across diverse fields, including engineering design and scientific modeling.