Deep operator network for surrogate modeling of poroelasticity with random permeability fields

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for probabilistic analysis, uncertainty quantification, and inverse problems. These simulations require repeated forward solves that are often prohibitively expensive, motivating the development of efficient surrogate models. However, efficient surrogate modeling techniques for poroelasticity with random permeability fields remain scarce. In this study, we propose a surrogate modeling framework based on the deep operator network (DeepONet), a neural architecture designed to learn mappings between infinite-dimensional function spaces. The proposed surrogate model approximates the solution operator that maps random permeability fields to transient poroelastic responses. To enhance predictive accuracy and stability, we integrate three strategies: nondimensionalization of the governing equations, input dimensionality reduction via Karhunen--Lo\'eve expansion, and a two-step training procedure that decouples the optimization of branch and trunk networks. The methodology is evaluated on two benchmark problems in poroelasticity: soil consolidation and ground subsidence induced by groundwater extraction. In both cases, the DeepONet achieves substantial speedup in inference while maintaining high predictive accuracy across a wide range of permeability statistics. These results highlight the potential of the proposed approach as a scalable and efficient surrogate modeling technique for poroelastic systems with random permeability fields.