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Reduced chaos expansions with random coefficients in reduced-dimensional stochastic modeling of coupled problems Arnst, Maarten ; ; et al in International Journal for Numerical Methods in Engineering (2014), 97 We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed ... [more ▼] We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed method entails a partitioned iterative solution algorithm that relies on a reduced-dimensional representation of information exchanged between subproblems to allow each subproblem to be solved within its own stochastic dimension while interacting with a reduced projection of the other subproblems. The proposed method extends previous work by the authors by introducing a reduced chaos expansion with random coefficients. The representation of the exchanged information by using this reduced chaos expansion with random coefficients enables an expeditious construction of doubly stochastic polynomial chaos expansions that separate the effect of uncertainty local to a subproblem from the effect of statistically independent uncertainty coming from other subproblems through the coupling. After laying out the theoretical framework, we apply the proposed method to a multiphysics problem from nuclear engineering. [less ▲] Detailed reference viewed: 52 (25 ULg)Stochastic Dimension Reduction of Multi Physics Systems through Measure Transformation ; ; et al Conference (2013, February 26) Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be ... [more ▼] Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be captured throughout the whole system, the so-called curse of dimensionality. We present techniques for mitigating the curse of dimensionality in network-coupled multiphysics systems by using the structure of the network to transform uncertainty representations as they pass between components. Examples from the simulation of nuclear power plants will be discussed. [less ▲] Detailed reference viewed: 90 (14 ULg)Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems Arnst, Maarten ; ; et al in International Journal for Numerical Methods in Engineering (2012), 92 Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼] Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower-dimensional space than the sources themselves. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲] Detailed reference viewed: 24 (12 ULg)Dimension reduction in stochastic modeling of coupled problems Arnst, Maarten ; ; et al in International Journal for Numerical Methods in Engineering (2012), 92 Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼] Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced-dimensional representation and in particular by an adaptation of the Karhunen-Loève decomposition. The effectiveness of the proposed dimension–reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲] Detailed reference viewed: 45 (16 ULg)Stochastic Dimension Reduction Techniques for Uncertainty Quantification of Multiphysics Systems ; Arnst, Maarten ; et al Conference (2012, April 02) Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be ... [more ▼] Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be captured throughout the whole system, the so-called curse of dimensionality. We present techniques for mitigating the curse of dimensionality in network-coupled multiphysics systems by using the structure of the network to transform uncertainty representations as they pass between components. Examples from the simulation of nuclear power plants will be discussed. [less ▲] Detailed reference viewed: 77 (8 ULg)Dimension Reduction and Measure Transformation in Stochastic Multiphysics Modeling Arnst, Maarten ; ; et al Conference (2012, April 02) We present a computational framework based on stochastic expansion methods for the efficient propagation of uncertainties through multiphysics models. The framework leverages an adaptation of the Karhunen ... [more ▼] We present a computational framework based on stochastic expansion methods for the efficient propagation of uncertainties through multiphysics models. The framework leverages an adaptation of the Karhunen-Loeve decomposition to extract a low-dimensional representation of information passed from component to component in a stochastic coupled model. After a measure transformation, the reduced-dimensional interface thus created enables a more efficient solution in a reduced-dimensional space. We demonstrate the proposed approach on an illustration problem from nuclear engineering [less ▲] Detailed reference viewed: 24 (2 ULg)Dimension Reduction and Measure Transformation in Stochastic Analysis of Coupled Systems Arnst, Maarten ; ; et al Scientific conference (2011, September 29) Detailed reference viewed: 45 (9 ULg)Dimension Reduction and Measure Transformation in Stochastic Simulations of Coupled Systems Arnst, Maarten ; ; et al Conference (2011, July 25) Detailed reference viewed: 25 (1 ULg)Uncertain Handshaking for Coupled Physics ; Arnst, Maarten ; et al Conference (2011, July 18) Detailed reference viewed: 30 (4 ULg)Random Handshaking and Information Recovery Between Scales and Models ; Arnst, Maarten ; et al Conference (2011, July 05) Detailed reference viewed: 27 (4 ULg)Dimension reduction and measure transformation in stochastic multiphysics modeling Arnst, Maarten ; ; et al Scientific conference (2011, March 31) Detailed reference viewed: 37 (7 ULg)Coupling Algorithms for Stochastic Multiphysics Arnst, Maarten ; ; et al Conference (2011, March 02) Detailed reference viewed: 25 (4 ULg) |
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