Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise

摘要

In this work, we extend upon the results of Raissi and Seshaiyer [A multi-fidelity stochastic collocation method for parabolic partial differential equations with random input data, Int. J. Uncertain. Quantif. 4(3) (2014), pp. 225-242]. In Raissi and Seshaiyer (2014), the authors propose to use deterministic model reduction techniques to enhance the performance of sampling methods like Monte-Carlo or stochastic collocation. However, in order to be able to apply the method proposed in Raissi and Seshaiyer (2014) to non-linear problems a crucial step needs to be taken. This step involves local improvements to reduced-order models. This paper is an illustration of the importance of this step. Local improvements to reduced-order models are achieved using sensitivity analysis of the proper orthogonal decomposition.