Physics Informed Deep Neural Networks for learning parameters with non-Gaussian non-stationary statistics

We present a physics informed Deep Neural Network (DNN) method for estimating parameters with arbitrary non-Gaussian non-stationary statistics in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs to approximate unknown parameters and constitutive relationships as well as states. The proposed approach increases the accuracy of DNN approximations of partially known functions when a limited number of measurements is available.