Fast and Flexible Uncertainty Quantification Through a Data-Driven Surrogate Model

To assess a computer model's descriptive and predictive power, the model's response to uncertainties in the input must be quantified. However, simulations of complex systems typically need a lot of computational resources, and thus prohibit exhaustive sweeps of high-dimensional spaces. Moreover, the time available to compute a result for decision systems is often very limited. In this paper, we construct a data-driven surrogate model from time delays of observations of a complex, microscopic model. We employ diffusion maps to reduce the dimensionality of the delay space. The surrogate model allows faster generation of the quantity of interest over time than the original, microscopic model. It is a nonintrusive method, and hence does not need access to the model formulation. In contrast to most other surrogate approaches, the construction allows quantities of interest that are not closed dynamically, because a closed state space is constructed through Takens delay embedding. Also, the surrogate can be stored to and loaded from storage with very little effort. The surrogate model is decoupled from the original model, and the fast execution speed allows us to quickly evaluate many different parameter distributions. We demonstrate the capability of the approach in combination with forward UQ on a parametrized Burgers' equation, and the microscopic simulation of a train station. The surrogate model can accurately capture the dynamical features in both examples, with relative errors always smaller than 10%. The simulation time in the real-world example can be reduced by an order of magnitude.