TY - JOUR
AU - Laurenti, Luca
AB - Abstract:In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input set of distributions close in the Wasserstein distance, we compute a set of distributions centered at a discrete distribution that is guaranteed to contain the pushforward of any distribution in the input set. Our approach is based on approximating a nominal distribution from the input set to a discrete support distribution for which the exact computation of the pushforward distribution is tractable, thus guaranteeing computational efficiency to our approach. Then, we rely on results from semi-discrete optimal transport and distributional robust optimization to show that for any $\epsilon > 0$ the error introduced by our approach can be made smaller than $\epsilon$. Critically, in the context of dynamical systems, we show how our results allow one to efficiently approximate the distribution of a stochastic dynamical system with a discrete support distribution for a possibly infinite horizon while bounding the resulting approximation error. We empirically investigate the effectiveness of our framework on various benchmarks, including a 10-D non-linear system, showing the effectiveness of our approach in quantifying uncertainty in linear and non-linear stochastic systems.
TI - Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance
JO - Mathematics
DO - 10.48550/arxiv.2506.08689
DA - 2025-06-11
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/efficient-uncertainty-propagation-with-guarantees-in-wasserstein-XonsERSTSr
VL - 2025
IS - 2506
DP - DeepDyve
ER -