Operator Learning for Consolidation: An Architectural Comparison for DeepONet Variants

TL;DR

This paper compares various DeepONet architectures for modeling consolidation in geotechnical engineering, introducing a Fourier feature-enhanced model that significantly improves accuracy and computational speed, especially in 3D scenarios.

Contribution

It systematically evaluates DeepONet variants for consolidation, proposing a Fourier feature-enhanced architecture that overcomes previous limitations and extends to 3D applications.

Findings

Model 3 outperforms standard DeepONets but struggles with high variation.

Model 4 captures rapidly varying functions effectively.

Speedup in 3D reaches approximately 1,000x compared to traditional solvers.

Abstract

Deep Operator Networks (DeepONets) have emerged as a powerful surrogate modeling framework for learning solution operators in PDE-governed systems. While their use is expanding across engineering disciplines, applications in geotechnical engineering remain limited. This study systematically evaluates several DeepONet architectures for the consolidation problem. We initially consider three architectures: a standard DeepONet with the coefficient of consolidation embedded in the branch net (Models 1 and 2), and a physics-inspired architecture with the coefficient embedded in the trunk net (Model 3). Results show that Model 3 outperforms the standard configurations (Models 1 and 2) but still has limitations when the target solution (excess pore pressures) exhibits significant variation. To overcome this limitation, we propose a Trunknet Fourier feature-enhanced DeepONet (Model 4) that addresses the identified limitations by capturing rapidly varying functions. We further extend Model 4 to 3D scenarios. Although the computational speedup can be modest in the 1D case (1.5-100x compared with traditional solvers), the speedup becomes more pronounced in 3D, reaching approximately 1,000x. Leveraging this efficiency, we offer a conceptual demonstration of DeepONet's potential to accelerate uncertainty quantification in a 3D consolidation problem. Overall, the study highlights the potential of DeepONets to enable efficient, generalizable surrogate modeling in geotechnical applications, advancing the integration of scientific machine learning in geotechnics, which is at an early stage.