Bayesian inference of parametric uncertainties is an attractive uncertainty quantification technique with its ability to seamlessly incorporate data as well as prior knowledge to update probability distributions over uncertain quantities. For complex systems with arbitrary posterior probabilities of parameters, Markov Chain Monte Carlo (MCMC) is the most commonly used method in Bayesian inference to evaluate the posterior parametric distribution. The main bottleneck, however, in applying Bayesian inference for complex systems, is that MCMC simulation involves evaluating complex models for 103 -105 realizations which becomes prohibitively expensive. Parallelization, a natural choice to reduce computational limitations, cannot be utilized as Markov chain Monte Carlo is a serial algorithm for which each new sample requires the knowledge of the previous sample in the parametric space.
Another way to reduce computational cost is to simplify the likelihood evaluation in posterior probability estimation by approximating the underlying physical models to make each step evaluation cheaper. With that motivation, there have been many different approaches studied in the past, such as as using low fidelity models applying a coarse spatial discretization , model approximation using global polynomials (polynomial chaos expansions) , reduced order models using proper orthogonal decomposition  and Gaussian approximation of the process , each with its own advantages and limitations in applicability.
In this work, we investigate the use of an artificial neural network (ANN) to develop a reduced order model in approximating the model output to apply in posterior evaluation of probabilities Using ANN as a reduced order model, the computational cost can by reduced drastically. Empirical models, in general, often fail to capture the behavior of the system over a wide range of parametric space. ANN, on the other hand can potentially represent wide regions of parametric variations as it has a learning capability which can be tuned for a large parametric space. We demonstrate the approach by applying it to estimate the impact of uncertainties of adsorption equilibrium parameters on the performance of a CO2 adsorption process using hollow fiber sorbents.
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