Transfer learning based physics-informed neural networks for solving inverse problems in tunneling
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Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained great prevalence in solving various scientific computing problems. This approach enables the solution of partial differential equations (PDEs) via embedding physical laws into the loss function of neural networks. Many inverse problems can also be tackled by simply combining the observational data from real life scenarios with existing PINN algorithms. In this paper, we present a multi-task learning method to improve the training stability of PINNs for linear elastic problems, and the homoscedastic uncertainty is introduced as a basis for weighting losses. Furthermore, we demonstrate an application of PINNs to a practical inverse problem in tunnel engineering: prediction of external loading distributions of tunnel rings based on a limited number of displacement monitoring points. To this end, we first determine a simplified tunneling scenario at the offline stage. By setting unknown boundary conditions as learnable parameters, PINNs can predict the external loads applied on the tunnel lining with the support of enough measurement data. When it comes to the online stage in real tunnel projects, the Kriging method is adopted to reconstruct the whole displacement field based on very limited measurements. Then transfer learning is employed to fine-tune the pre-trained model from offline stage. Our results show that, although the reconstructed displacement field generated from gappy measurements is accompanied by errors, satisfactory results can still be obtained from the PINN model due to the dual regularization of physics laws and prior knowledge, which exhibits better robustness compared to traditional analysis methods. The convergence of training is also accelerated, thus making it possible for PINNs to be applied in actual tunnel projects.
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