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.