How physics-informed neural networks can leverage our understanding of conventional geotechnical and structural engineering problems?

  • Vahab, Mohammad (UNSW)
  • Khalili, Nasser (UNSW)

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Physics-Informed Neural Networks (PINNs) are a class of Deep Learning (DL) that incorporate a series of physical laws, frequently described in the form of partial differential equations (PDEs), to steer the learning towards the solution for sparse training datasets, which could not be plausible with classic DL algorithms. The prosperity of PINNs is attributed to substantial algorithmic advances (e.g., graph-based automated differentiation) and major software developments (e.g., TensorFlow , Keras). DL is best suited to recognize the mapping relations between inputs/outputs given a training dataset. A beneficial remedy can be offered by physics-informed deep learning, which provides the network model along with the laws of physics governing the system. This can rectify the issues associated with the missing ingredients induced by the sparsity of data, uncertainties, or other less understood factors. We explore the application of the Physics-Informed Neural Networks (PINNs) in a range of conventional geotechnical and structural engineering problems. An Airy-inspired PINNs solution is proposed for the analysis of foundation problems. As another improvement, Fourier series are elaborated to investigate the solution of plates deflection. We find that enriching the feature space using Airy stress functions/Fourier series can significantly improve the accuracy of PINN solutions for biharmonic PDEs. We construct custom physics-informed functions next which pertain to fundamental solutions of fracture mechanics. We show the proposed framework can easily captures the singular solution and characteristic parameters accurately on both noise-free and noisy data regimes. Finally, the application PINNs to forward and inverse analyses of pile-soil interaction problems is presented.