This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification problems. First, DNNs are known to be too complex that they can easily overfit the training data. Second, the selection of the input regressors for system identification is nontrivial. Third, uncertainty quantification of the model parameters and predictions are necessary. The proposed Bayesian approach offers a principled way to alleviate the above challenges by marginal likelihood/model evidence approximation and structured group sparsity-inducing priors construction. The identification algorithm is derived as an iterative regularized optimization procedure that can be solved as efficiently as training typical DNNs. Furthermore, a practical calculation approach based on the Monte-Carlo integration method is derived to quantify the uncertainty of the parameters and predictions. The effectiveness of the proposed Bayesian approach is demonstrated on several linear and nonlinear systems identification benchmarks with achieving good and competitive simulation accuracy.
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