Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution

In this article, we present a novel data assimilation strategy in pore-scale imaging and demonstrate that this makes it possible to robustly address reactive inverse problems incorporating Uncertainty Quantification (UQ). Pore-scale modeling of reactive flow offers a valuable opportunity to investigate the evolution of macro-scale properties subject to dynamic processes in the context of Carbon Capture and Storage (CCS). Yet, they suffer from imaging limitations arising from the associated X-ray microtomography (X-ray \(\mu \)CT) process, which induces discrepancies in the properties estimates. Assessment of the kinetic parameters also raises challenges, as reactive coefficients are critical parameters that can cover a wide range of values. We account for these two issues and ensure reliable calibration of pore-scale modeling, based on dynamical \(\mu \)CT images, by integrating uncertainty quantification in the workflow. The present method is based on a multitasking formulation of reactive inverse problems combining data-driven and physics-informed techniques in calcite dissolution. This allows quantifying morphological uncertainties on the porosity field and estimating reactive parameter ranges through prescribed PDE models, with a latent concentration field, and dynamical \(\mu \)CT observations. The data assimilation strategy relies on sequential reinforcement incorporating successively additional PDE constraints and suitable formulation of the heterogeneous diffusion differential operator leading to enhanced computational efficiency. We provide a robust and unbiased uncertainty quantification by straightforward adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), ensuring reliable micro-porosity changes during geochemical transformations. We demonstrate successful Bayesian Inference in 1D+Time calcite dissolution based on synthetic \(\mu \)CT images with meaningful posterior distribution on the reactive parameters and dimensionless numbers. We eventually apply this framework to a more realistic 2D+Time data assimilation problem involving heterogeneous porosity levels and synthetic \(\mu \)CT dynamical observations.