Laplace fPINNs

Laplace approximations offer a computationally efficient way to estimate uncertainty in complex models like deep neural networks, particularly in Bayesian deep learning and physics-informed neural networks (PINNs). Current research focuses on improving the accuracy and scalability of Laplace methods, including exploring function-space priors to incorporate prior knowledge and developing online variants for efficient hyperparameter optimization. These advancements are impacting diverse fields, enabling more robust uncertainty quantification in scientific inference tasks, such as solving fractional diffusion equations and hypocenter localization, and improving model selection in various applications.