Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Using stochastic analysis to capture unstable equilibrium in natural convection
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Journal of Computational Physics
Performance evaluation of generalized polynomial chaos
ICCS'03 Proceedings of the 2003 international conference on Computational science
Journal of Computational Physics
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
Journal of Computational Physics
A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis
SIAM Journal on Numerical Analysis
Uncertainty quantification in hybrid dynamical systems
Journal of Computational Physics
Bayesian estimates of parameter variability in the k-ε turbulence model
Journal of Computational Physics
Hi-index | 31.47 |
Experimental evidence suggests that the dynamics of many physical phenomena are significantly affected by the underlying uncertainties associated with variations in properties and fluctuations in operating conditions. Recent developments in stochastic analysis have opened the possibility of realistic modeling of such systems in the presence of multiple sources of uncertainties. These advances raise the possibility of solving the corresponding stochastic inverse problem: the problem of designing/estimating the evolution of a system in the presence of multiple sources of uncertainty given limited information. A scalable, parallel methodology for stochastic inverse/design problems is developed in this article. The representation of the underlying uncertainties and the resultant stochastic dependant variables is performed using a sparse grid collocation methodology. A novel stochastic sensitivity method is introduced based on multiple solutions to deterministic sensitivity problems. The stochastic inverse/design problem is transformed to a deterministic optimization problem in a larger-dimensional space that is subsequently solved using deterministic optimization algorithms. The design framework relies entirely on deterministic direct and sensitivity analysis of the continuum systems, thereby significantly enhancing the range of applicability of the framework for the design in the presence of uncertainty of many other systems usually analyzed with legacy codes. Various illustrative examples with multiple sources of uncertainty including inverse heat conduction problems in random heterogeneous media are provided to showcase the developed framework.