Physics-informed deep learning for one-dimensional consolidation

Neural networks with physical governing equations as constraints have recently created a new trend in machine learning research. In this context, a review of related research is first presented and discussed. The potential offered by such physics-informed deep learning models for computations in geomechanics is demonstrated by application to one-dimensional (1D) consolidation. The governing equation for 1D problems is applied as a constraint in the deep learning model. The deep learning model relies on automatic differentiation for applying the governing equation as a constraint, based on the mathematical approximations established by the neural network. The total loss is measured as a combination of the training loss (based on analytical and model predicted solutions) and the constraint loss (a requirement to satisfy the governing equation). Two classes of problems are considered: forward and inverse problems. The forward problems demonstrate the performance of a physically constrained neural network model in predicting solutions for 1D consolidation problems. Inverse problems show prediction of the coefficient of consolidation. Terzaghi's problem, with varying boundary conditions, is used as a numerical example and the deep learning model shows a remarkable performance in both the forward and inverse problems. While the application demonstrated here is a simple 1D consolidation problem, such a deep learning model integrated with a physical law has significant implications for use in, such as, faster realtime numerical prediction for digital twins, numerical model reproducibility and constitutive model parameter optimization. (C) 2021 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V.

Automated summary

This study introduces a new trend in machine learning research, where neural networks with physical governing equations as constraints have shown potential in geomechanics. By applying these models to 1D consolidation problems, the study demonstrates their performance and implications for faster numerical prediction and model optimization.