We present the preliminary results of a Physics-Informed Neural Network (PINN) for a Wigner-Fokker-Planck (WFP) equation modeling open quantum systems such as electron transport in semiconductors. The WFP equation is a mathematical model that considers diffusion and friction introduced by the environment into an open quantum (sub-)system, describing the problem via a continuous quantum variable formulation. Recent developments in scientific machine learning have demonstrated that PINNs are useful in providing data-driven solutions to partial differential equations (PDE) and for data-driven discovery [20] in the estimation of model parameters, particularly when constrained to small or noisy data. PINNs minimize a residual additional to the typical Neural Network approach related to the satisfaction of a PDE that represents the “Physics” of the problem, along with the traditional loss function that estimates the fit to the data. The former residual implicitly trains the model to respect conservation principles following from the PDE that models the Physics phenomena. Since optimization is not solely dependent on minimizing the fit to the training data, such as in traditional machine learning models, it can perform exceedingly well for inverse problems to estimate model parameters, such as the diffusion and friction parameters in the particular case of our Wigner-Fokker-Planck model, when constrained to small data. This work used the PINN methodology to solve a data-driven discovery problem for the Wigner-Fokker-Planck equation. In particular, we solved an inverse problem with synthetic data obtained from a Monte Carlo forward solver of the Wigner-Fokker-Planck equation to estimate the elements of our diffusion matrix as parameters of the model representing noise introduced by the environment into the open quantum system.