\(\Pi\)4U: a high performance computing framework for Bayesian uncertainty quantification of complex models. (English) Zbl 1352.65009
Summary: We present {\(\Pi\)}4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.
MSC:
| 65C05 | Monte Carlo methods |
| 62F15 | Bayesian inference |
| 65Y10 | Numerical algorithms for specific classes of architectures |
| 65Y15 | Packaged methods for numerical algorithms |
| 82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
| 76T25 | Granular flows |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
Keywords:
uncertainty quantification; parallel computing; distributed computing; Bayesian inference; reliabilityReferences:
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