In-Poro-DON: a differentiable inversion framework for poroelasticity powered by deep operator networks

Poroelasticity inversion aims to infer subsurface material properties, including permeability and drained bulk modulus, from observed pore pressures and solid displacements. Conventionally, this requires executing forward numerical solvers thousands of times with varying material properties until simulated responses align with the observations. Such repetitive simulations are computationally expensive and constitute the main bottleneck of the inversion. To this end, we propose a differentiable modeling-based framework for poroelasticity inversion, which embeds DeepONet surrogates into a differentiable inversion framework. The surrogates approximate the mappings from material properties to poroelasticity responses, which achieve up to a 100-fold speedup over the finite-difference solver while maintaining satisfactory accuracy ($R^2$> 0.999). During inversion, the unknown material properties are treated as trainable components and passed through the DeepONet surrogates to predict poroelasticity responses. The mismatch between these predictions and the observations is then minimized to update the material property estimates through gradient-based optimization. The proposed framework was evaluated using four experimental and numerical benchmarks, covering 1-D and 2-D scenarios as well as homogeneous and heterogeneous material properties. Across these cases, the proposed framework accurately infers material properties with R^2 >= 0.883 and shows favorable accuracy and computational efficiency relative to the tested alternatives under the benchmark settings.