High Dimensional Uncertainty

High-dimensional uncertainty quantification (UQ) tackles the challenge of efficiently characterizing and managing uncertainty in systems with numerous random input parameters, a common problem in complex simulations and real-world applications. Current research focuses on developing efficient surrogate models, such as neural operators, Gaussian processes, and deep learning architectures like U-nets, often incorporating dimension reduction techniques to mitigate the "curse of dimensionality." These advancements enable more accurate and computationally feasible UQ in diverse fields, including engineering design, autonomous vehicle safety, and scientific computing, leading to improved decision-making under uncertainty.