Enhanced DeepONet for 1-D consolidation operator learning: an architectural investigation

2025-07-14

AI Summary

DeepONet suffers from reduced accuracy in modeling one-dimensional soil consolidation due to highly oscillatory excess pore-water pressure fields. Method: We propose a Fourier-feature-enhanced DeepONet architecture, embedding frequency-domain priors into the trunk network to improve representation of rapidly varying solutions; the branch-trunk structure is further guided by physics-informed design to construct an efficient PDE surrogate model. Results: Experiments demonstrate that the proposed method maintains high accuracy while accelerating inference by 1.5–100× over conventional explicit and implicit solvers; Model 4 achieves the best overall performance. This work significantly enhances the applicability and reliability of scientific machine learning for transient, multiscale problems in geotechnical engineering.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

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: Models for Web evolution

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 one-dimensional 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. All proposed architectures achieve speedups ranging from 1.5 to 100 times over traditional explicit and implicit solvers, with Model 4 being the most efficient. Larger computational savings are expected for more complex systems than the explored 1D case, which is promising. 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.

Problem

• Evaluating DeepONet architectures for 1D consolidation problem
• Improving accuracy for rapidly varying pore pressure solutions
• Achieving computational speedup over traditional solvers

Innovation

• Enhanced DeepONet for consolidation operator learning
• Trunknet Fourier feature-enhanced DeepONet architecture
• Achieves 1.5 to 100 times speedup over solvers