Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1404854
- Report Number(s):
- LLNL-TR-740300
- Country of Publication:
- United States
- Language:
- English
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