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

Ground settlement prediction during mechanized tunneling is of paramount importance and remains a challenging research topic. Typically, two paradigms are existing: a physics-driven approach utilizing numerical simulation models for prediction, and a data -driven approach employing machine learning techniques to learn mappings between influencing factors and the 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. The results show that the proposed method can effectively capture the physical information provided by the numerical simulations and accurately fit measured data (R2 around 0.9) as well. Notably, even when dealing with very limited noisy monitoring data (with a 50% error), the proposed model remains robust, achieving satisfactory results with R2 > 0.8. In comparison, the R2 score obtained by pure simulation -based prediction is only 0.2. The utilization of transfer learning significantly reduces the training time from 20 min to within 30 s, showcasing the potential of our method for real -time settlement prediction during tunnel construction.