Because of the many uncertainties associated with most flow and transport parameters, studies often implement the numerical simulations within a Monte Carlo frame of work. The large numbers of realizations needed to achieve convergence for the statistics of concern make the Monte Carlo approach computationally demanding. In this study we attempt to develop an empirical-numerical approach to generate Lagrangian particle trajectories in two-dimensional domain given a certain input heterogeneity model without repeatedly solving the flow equation for each realization, with the purpose of evaluating ensemble plume statistics. Artificial neural networks are used to map the relationship between the particle trajectories and the physical properties of the formation. This is achieved by training the neural network through a set of sufficient examples derived from a few realizations using an exponential log-K covariance. The trained network is then used to predict particle trajectories in heterogeneity characterized by an exponential, a Gaussian, a hole-type, or a fractal covariance model. The network that is trained using the exponential model successfully predicts transport results for other models with high accuracy and low computational effort. Accuracy of prediction of the trajectory (percent of explained variance) reaches 94% in the direction of mean flow and 91% normal to it. For the cases studied here, the speed of calculation is ~7.8 times faster than the traditional approach for 1000 realizations. As the number of realizations increases, the speed factor approaches 12.8. Solute mass flux (mean and standard deviation) and mean-plume concentrations predicted by the trained network agree very closely with the target result obtained via traditional Monte Carlo simulations. ¿ 2001 American Geophysical Union