Epilogue

Abstract

In the preceding chapters theoretical developments were presented of uncertainty propagation and quantification methods. The fundamental approach generally adopted in this monograph is based on the development of spectral representations of the input data and model solution, and on exploiting these representations in the construction of numerical methods and computational algorithms for the solution and analysis of stochastic systems. Application of these methods was illustrated through elementary examples as well as more involved problems from incompressible and weakly compressible flow. In conclusion, we provide a brief discussion of selected topics, which we attempt to group into the following (somewhat connected) categories: (a) potential extensions of methodologies outlined in previous chapters, (b) open problems, and (c) new desirable capabilities.