(5)

Accurate prediction of ground surface settlement (GSS) adjacent to an excavation is important to prevent potential damage to the surrounding environment. Previous studies have extensively delved into this topic but all under the limitations of either imprecise theories or insufficient data. In the present study, we proposed a physics-constrained neural network (PhyNN) for predicting excavation-induced GSS to fully integrate the theory of elasticity with observations and make full use of the strong fitting ability of neural networks (NNs). This model incorporates an analytical solution as an additional regularization term in the loss function to guide the training of NN. Moreover, we introduced three trainable parameters into the analytical solution so that it can be adaptively modified during the training process. The performance of the proposed PhyNN model is verified using data from a case study project. Results show that our PhyNN model achieves higher prediction accuracy, better generalization ability, and robustness than the purely data-driven NN model when confronted with data containing noise and outliers. Remarkably, by incorporating physical constraints, the admissible solution space of PhyNN is significantly narrowed, leading to a substantial reduction in the need for the amount of training data. The proposed PhyNN can be utilized as a general framework for integrating physical constraints into data-driven machine-learning models. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

来源平台：JOURNAL OF ROCK MECHANICS AND GEOTECHNICAL ENGINEERING