Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by uncertainty in their parameters. The polynomial chaos method is a computational approach to solve stochastic partial differential equations (SPDE) by projecting the solution onto a space of orthogonal polynomials of the stochastic variables and solving for the deterministic coefficients. Polynomial chaos can be more efficient than Monte Carlo methods when the number of stochastic variables is low, and the integration time is not too large. When performing long-term integration, however, achieving accurate solutions often requires the space of polynomial functions to become unacceptably large. This talk will introduce alternative approach, where sets of empirical basis functions are constructing by examining the behavior of the solution for fixed values of the random variables. The empirical basis functions are evolved over time, which means that the total number of basis functions can be kept small, even when performing long-term integration.