Operator Learning for Consolidation: An Architectural Comparison for DeepONet Variants
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 27 of its 54 references that are in the map. First posted on arXiv 14 Jul 2025.
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References · 27
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- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
- 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
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- 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 284
- 2022MIONet: Learning multiple-input operators via tensor productcited by 181
15 more
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- 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
- 2022Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizationscited by 27
- 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
- 2020Deep Learning for One-dimensional Consolidationcited by 14
- 2023A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel constructioncited by 12
- 2024Advanced Deep Operator Networks to Predict Multiphysics Solution Fields in Materials Processing and Additive Manufacturingcited by 12
- 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
- 2022Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functionscited by 11
- 2023Benign Oscillation of Stochastic Gradient Descent with Large Learning Ratescited by 8
- 2023Real-Time Prediction of Gas Flow Dynamics in Diesel Engines using a Deep Neural Operator Frameworkcited by 5
- 2024What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applicationscited by 3
- 2024Physics-informed DeepONet with stiffness-based loss functions for structural response predictioncited by 1
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