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

2025-09-15

AI Summary

Forward poroelastic simulations under stochastic permeability fields incur prohibitive computational costs, and efficient surrogate models remain scarce. Method: This paper proposes a Deep Operator Network (DeepONet)-based surrogate modeling framework, incorporating nondimensionalization, Karhunen–Loève expansion for dimensionality reduction, and a two-stage training strategy to enhance generalization and training stability for high-dimensional random inputs. Contribution/Results: The approach achieves the first efficient learning of the transient poroelastic response operator. Validated on two canonical benchmarks—soil consolidation and groundwater withdrawal-induced subsidence—it delivers high predictive accuracy across diverse permeability statistics. Inference is accelerated by 2–3 orders of magnitude relative to conventional numerical solvers, enabling direct integration into downstream tasks such as uncertainty quantification and parameter inversion.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

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--Loéve 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.

Problem

• Surrogate modeling for poroelasticity with random permeability fields
• Learning mappings between infinite-dimensional function spaces
• Approximating solution operator for transient poroelastic responses

Innovation

• DeepONet for surrogate modeling
• Nondimensionalization and dimensionality reduction
• Two-step training procedure optimization