An inverse parameter identification procedure assessing the quality of the estimates using Bayesian neural networks

The paper proposes a general procedure based on Bayesian neural networks for parameter identification of numerical models. In this context, the Bayesian neural networks are extended to multiple outputs with a full covariance matrix to describe the correlation between the noise of output parameters. This extension is especially useful for inverse problems such as a parameter identification procedure, since it allows for the quantification of correlations between output parameters. Based on numerically obtained forward calculations, the Bayesian neural network is trained to solve the inverse parameter identification problem. The main advantage of the method is the ability to verify the accuracy of the identified parameters and their correlation. The methodology further allows to detect, whether a certain set of experiments is sufficient to determine an individual model parameter. As a result, a general scheme for the design of experiments to identify model parameters is developed and illustrated for two examples.