Surrogate-Based Strategies for Accelerated Bayesian Calibration of Computer Codes With Complete Maximum a Posteriori Estimation of Model Error

Abstract The calibration of a computer code is a process that reduces the uncertainty of model parameters by matching the code’s predictions to experimental observations of a quantity of interest. A more faithful representation of the global uncertainty is achieved by including a model error term, a discrepancy between the physical system and the computer code. The recently proposed complete maximum a posteriori (CMP) method is able to infer both a posterior distribution of the model parameters and a model error term, improving upon traditional frameworks. On the other hand, the CMP method relies on an optimization step which increases the cost of complex calibration problems. This article proposes a surrogate-based strategy to reduce the computational cost of the CMP method. First, we build a surrogate model of the model error’s hyperparameters using Gaussian processes. Second, we propose an iterative algorithm that builds a training set in regions of the parameter space that are more likely, reducing the overall cost of the algorithm and improving the accuracy of the surrogate. The proposed strategy is applied to four different examples, including a design problem in solid mechanics and a complex test case in fluid dynamics. The results show that the proposed strategy is able to accelerate the CMP method without losing accuracy, making it suitable for real-world applications. In an industrial application, we demonstrate a speed-up of almost 100 compared to the original CMP method.