Bayesian Inversion

Bayesian inversion is a statistical framework for solving inverse problems, aiming to estimate unknown parameters or inputs from observed data by incorporating prior knowledge and quantifying uncertainty in the estimates. Current research emphasizes developing efficient algorithms, such as those leveraging neural networks (e.g., generative models, neural operators) and Markov Chain Monte Carlo methods, to handle complex forward models and high-dimensional data in diverse applications. This approach is significantly impacting fields ranging from geophysical imaging and medical imaging to fluid dynamics and materials science by providing more robust and reliable solutions with associated uncertainty quantification.