High Dimensional Inverse Problem

High-dimensional inverse problems aim to infer unknown parameters from limited and noisy observations, often governed by complex physical models. Current research focuses on developing efficient and robust Bayesian inference methods, employing neural networks (e.g., variational autoencoders, score-based diffusion models, and physics-informed neural networks) to approximate posterior distributions and handle high dimensionality. These advancements are crucial for tackling challenging problems across diverse scientific domains, such as material characterization, geophysical imaging, and uncertainty quantification in complex systems, by enabling more accurate and computationally feasible solutions. The development of data-efficient methods and improved uncertainty quantification are key ongoing research directions.