Data-Consistent Solutions to Stochastic Inverse Problems Using a Probabilistic Multi-Fidelity Method Based on Conditional Densities
- Technical Univ. of Munich (Germany)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
In this work, we build upon a recently developed approach for solving stochastic inverse problems based on a combination of measure-theoretic principles and Bayes' rule. We propose a multi-fidelity method to reduce the computational burden of performing uncertainty quantification using high-fidelity models. This approach is based on a Monte Carlo framework for uncertainty quantification that combines information from solvers of various fidelities to obtain statistics on the quantities of interest of the problem. In particular, our goal is to generate samples from a high-fidelity push-forward density at a fraction of the costs of standard Monte Carlo methods, while maintaining flexibility in the number of random model input parameters. Key to this methodology is the construction of a regression model to represent the stochastic mapping between the low- and high-fidelity models, such that most of the computations can be leveraged to the low-fidelity model. To that end, we employ Gaussian process regression and present extensions to multi-level-type hierarchies as well as to the case of multiple quantities of interest. Finally, we demonstrate the feasibility of the framework in several numerical examples.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); German Research Foundation (DFG)
- Grant/Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1769923
- Report Number(s):
- SAND--2021-2082J; 694019
- Journal Information:
- International Journal for Uncertainty Quantification, Journal Name: International Journal for Uncertainty Quantification Journal Issue: 5 Vol. 10; ISSN 2152-5080
- Publisher:
- Begell HouseCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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