In-Poro: Differentiable Inverse Analysis Framework for Poroelasticity

Numerical poroelasticity models are key tools for designing, operating, and managing many subsurface technologies, such as geothermal energy extraction and geologic carbon storage. The major challenge in applying these models is to calibrate spatially heterogeneous material properties (e.g., drained bulk modulus and permeability) based on observed poroelasticity responses (e.g., solid displacement and pore pressure). To address this challenge, we present In-Poro, to the best of our knowledge the first differentiable modeling-based inverse analysis framework for poroelasticity problems. It can infer spatial distributions of material properties from observed solid displacements and pore pressures, instead of a few constant material properties as could be done by traditional inverse analysis. In-Poro represents unknown material properties using physics-constrained neural networks (PCNNs), which have strong learning capabilities and can encode any constraint or prior knowledge. These material properties, represented by PCNNs, are embedded into a finite-difference-based poroelasticity solver to predict the spatiotemporal variations of solid displacement and pore pressure. The mismatch between these predictions and observations is utilized as a loss function, which guides the end-to-end training of PCNNs. By tightly coupling the physics-based solver with PCNNs, In-Poro achieves clear interpretability and expressive learning capabilities. To examine its effectiveness, In-Poro was applied to one realistic consolidation experiment and two widely accepted numerical benchmark problems, which span from one-dimensional to two-dimensional domains and from homogeneous materials to heterogeneous materials. In all of these problems, In-Poro achieved excellent accuracy (R2>0.99) in both inferring unknown material properties and reconstructing observations. Even under sparse and noisy observations, In-Poro maintained robust performance (R2>0.97).