A Comparative Study of Effective Surface Relaxation Estimation Using Two NMR Relaxometry Inverse Modeling Approaches

This talk presents a comparative analysis of two advanced inverse modeling approaches for estimating the properties of porous media from NMR relaxometry signals. While inverse NMR relaxometry (T₁/T₂ distribution recovery) is a fundamental technique for characterizing pore-scale structures based on surface-influenced molecular relaxation, the choice of inversion methodology has a critical impact on the reliability and efficiency of the results. We specifically evaluate a rigorous Bayesian framework with Markov Chain Monte Carlo sampling (MCMC) against a modern Physics-Informed Neural Network (G-PINN) based on a Galerkin formulation. The comparison is made in terms of numerical accuracy, uncertainty quantification, and computational performance. Using synthetic NMR relaxometry signals, generated from both analytical and direct numerical models, the two approaches for estimating the effective surface relaxation are compared. The details of the complete methodological process are presented, encompassing mathematical formulations, numerical discretizations, and computational implementations, providing a guide for selecting an inversion approach tailored to the quality of the data and the specific requirements of the application.