Multifidelity methods for uncertainty quantification of a nonlocal model for phase changes in materials
This study is devoted to the construction of a multifidelity Monte Carlo (MFMC) method for the uncertainty quantification of a nonlocal, non-mass-conserving Cahn-Hilliard model for phase transitions with an obstacle potential. Here, we are interested in estimating the expected value of an output of interest (OoI) that depends on the solution of the nonlocal Cahn-Hilliard model. As opposed to its local counterpart, the nonlocal model captures sharp interfaces without the need for significant mesh refinement. However, the computational cost of the nonlocal Cahn-Hilliard model is higher than that of its local counterpart with similar mesh refinement, inhibiting its use for outer-loop applications such as uncertainty quantification. The MFMC method augments the desired high-fidelity, high-cost OoI with a set of lower-fidelity, lower-cost OoIs to alleviate the computational burden associated with nonlocality. Most of the computational budget is allocated to sampling the cheap surrogate models to achieve speedup, whereas the high-fidelity model is sparsely sampled to maintain accuracy. For the non-mass-conserving nonlocal Cahn-Hilliard model, the use of the MFMC method results in, for a given computational budget, about an order of magnitude reduction in the mean-squared error of the expected value of the OoI relative to that of the Monte Carlo method.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Univ. of Texas, Austin, TX (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC05-00OR22725; SC0019303; SC0021077; SC0023171
- OSTI ID:
- 2329600
- Alternate ID(s):
- OSTI ID: 2326096
- Journal Information:
- Computers and Structures, Journal Name: Computers and Structures Journal Issue: 1 Vol. 297; ISSN 0045-7949
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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