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A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models
Finite Elements in Analysis and Design (2008)
  • Baskar Ganapathysubramanian, Cornell University
  • Nicholas Zabaras, Cornell University
Many physical systems of fundamental and industrial importance are significantly affected by the underlying fluctuations/variations in boundary, initial conditions as well as variabilities in operating and surrounding conditions. There has been increasing interest in analyzing and quantifying the effects of uncertain inputs in the solution of partial differential equations that describe these physical phenomena. Such analysis naturally leads to a rigorous methodology to design/control physical processes in the presence of multiple sources of uncertainty. A general application of these ideas to many significant problems in engineering is mainly limited by two issues. The first is the significant effort required to convert complex deterministic software/legacy codes into their stochastic counterparts. The second bottleneck to the utility of stochastic modeling is the construction of realistic, viable models of the input variability. This work attempts to demystify stochastic modeling by providing easy-to-implement strategies to address these two issues. In the first part of the paper, strategies to construct realistic input models that encode the variabilities in initial and boundary conditions as well as other parameters are provided. In the second part of the paper, we review recent advances in stochastic modeling and provide a road map to trivially convert any deterministic code into its stochastic counterpart. Several illustrative examples showcasing the ease of converting deterministic codes to stochastic codes are provided.
  • Stochastic partial differential equations,
  • Deterministic simulators,
  • Random processes,
  • Stochastic collocation,
  • Data driven models,
  • Sparse grids,
  • Random heterogeneous media,
  • Microstructures,
  • Model reduction
Publication Date
March, 2008
Publisher Statement
This is a manuscript of an article from Finite Elements in Analysis and Design 44 (2008): 298, doi:10.1016/j.finel.2007.11.015. Copyright 2007 Elsevier B.V. Posted with permission.
Citation Information
Baskar Ganapathysubramanian and Nicholas Zabaras. "A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models" Finite Elements in Analysis and Design Vol. 44 Iss. 5 (2008) p. 298 - 320
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Creative Commons License
This work is licensed under a Creative Commons CC_BY-NC-ND International License.