From space weather, to climate, considerable efforts are being made to improve the accuracy of the physics models. These models have complex interactions between physical phenomena evolving at different scales. Reliability of such multi-physics models remains a grand challenge. For example, an important research question is how will precipitation evolve over the next 40 years? When physical phenomena interact, the predictions from such models get polluted and the inherent uncertainties are compounded, thus reducing their reliability. To tackle this problem, we look at a novel approach for uncertainty quantification (UQ) in coupled systems by learning the mathematical operators, called the Perron-Frobenius and Koopman operators, that describe the propagation of uncertainties in such models. While scale bridging of multi-scale physics has received considerable attention, UQ of multi-physics remain a challenge. Existing methods for UQ don't quantify the stochastic nature of interaction in multi-physics models. The key scientific contributions of our work is the development of a novel UQ method that 1) quantifies the stochastic nature of coupling, 2) is non-intrusive and, 3) provides both forward and backward UQ in coupled systems. We leverage special stochastic operators called the Perron-Frobenius and Koopman Operators that act on functions of the model state and describe the evolution of probability densities forward and backward in time respectively. Even when the models are non-linear, this evolution of probability is governed by a linear Partial Differential Equation. However, in the presence of data from disparate sources for complex systems, solving the governing equations for such operators may not be feasible. In this talk we will focus on the propagation of uncertainties and the use of Koopman operators for data assimilation.