Auto-weighted Bayesian Physics-Informed Neural Networks and robust
  estimations for multitask inverse problems in pore-scale imaging of
  dissolution
Sarah Perez Philippe Poncet
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. Yet, they suffer from imaging limitations arising from the
associated X-ray microtomography (X-ray microCT) 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 microCT 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 microCT. The data
assimilation strategy relies on sequential reinforcement incorporating
successively additional PDE constraints. We guarantee 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 and 2D+Time calcite dissolution based on synthetic microCT
images with meaningful posterior distribution on the reactive parameters and
dimensionless numbers.