Efficient uncertainty propagation for network multiphysics systems

We consider a multiphysics system with multiple component models coupled together through network coupling interfaces, i.e., a handful of scalars. If each component model contains uncertainties represented by a set of parameters, a straightfoward uncertainty quantification (UQ) study would collect all uncertainties into a single set and treat the multiphysics model as a black box. Such an approach ignores the rich structure of the multiphysics system, and the combined space of uncertainties can have a large dimension that prohibits the use of polynomial surrogate models. We propose an intrusive methodology that exploits the structure of the network coupled multiphysics system to efficiently construct a polynomial surrogate of the model output as a function of uncertain inputs. Using a nonlinear elimination strategy, we treat the solution as a composite function: the model outputs are functions of the coupling terms which are functions of the uncertain parameters. The composite structure allows us to construct and employ a reduced polynomial basis that depends on the coupling terms; the basis can be constructed with many fewer system solves than the naive approach, which results in substantial computational savings. We demonstrate the method on an idealized model of a nuclear reactor.