Weighted reduced order methods for parametrized partial differential equations with random inputs
This work addresses the need for efficient reduced-order modeling of stochastic PDEs, but the contribution is incremental as it extends existing weighted methods to random inputs.
The authors propose weighted reduced order methods (weighted reduced basis and weighted proper orthogonal decomposition) for parametrized PDEs with random inputs, demonstrating efficiency on an elasticity problem.
In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.