We present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models in the presence of partial data. In particular, we will concentrate on the problem of estimating the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation. For the parameter estimation problem, we assume that partial measurements of the coefficient and states are available and demonstrate that under these conditions, the proposed method is more accurate than state-of-the-art methods e.g. Maximum a posteriori estimation. Finally, we present a systematic study of the method and demonstrate that the proposed method remains accurate in the presence of measurement noise.

Biography: Carlos' research interests include machine learning, quantum computation, and graph theory. He received his PhD in Mathematics from the University of Houston and is currently a Postdoctoral Research Associate at Pacific Northwest National Laboratory.