# A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel construction

arXiv: https://arxiv.org/abs/2310.00057 · HTML: https://mlsanity.com/paper/2310.00057/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2023.

## Built on by (most cited first, 12 of 12)

- [TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation](https://mlsanity.com/paper/2505.17341/) (2025)
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- [Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks](https://mlsanity.com/paper/2503.17402/) (2025)
- [A Critical Assessment of PINNs and Operator Learning for Geotechnical Engineering](https://mlsanity.com/paper/2512.24365/) (2025)
- [Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty](https://mlsanity.com/paper/2506.11761/) (2025)
- [Operator Learning for Consolidation: An Architectural Comparison for DeepONet Variants](https://mlsanity.com/paper/2507.10368/) (2025)
- [Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks](https://mlsanity.com/paper/2512.04434/) (2025)
- [Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges](https://mlsanity.com/paper/2606.20015/) (2026)

## Abstract (arXiv)

Ground settlement prediction during the process of mechanized tunneling is of paramount importance and remains a challenging research topic. Typically, two paradigms are existing: a physics-driven approach utilizing process-oriented computational simulation models for the tunnel-soil interaction and the settlement prediction, and a data-driven approach employing machine learning techniques to establish mappings between influencing factors and the ground settlement. To integrate the advantages of both approaches and to assimilate the data from different sources, we propose a multi-fidelity deep operator network (DeepONet) framework, leveraging the recently developed operator learning methods. The presented framework comprises of two components: a low-fidelity subnet that captures the fundamental ground settlement patterns obtained from finite element simulations, and a high-fidelity subnet that learns the nonlinear correlation between numerical models and real engineering monitoring data. A pre-processing strategy for causality is adopted to consider the spatio-temporal characteristics of the settlement during tunnel excavation. Transfer learning is utilized to reduce the training cost for the low-fidelity subnet. The results show that the proposed method can effectively capture the physical information provided by the numerical simulations and accurately fit measured data as well. Remarkably, even with very limited noisy monitoring data, the proposed model can achieve rapid, accurate, and robust predictions of the full-field ground settlement in real-time during mechanized tunnel excavation.