Sparse Bayesian deep learning for dynamic system identification

Sparse Bayesian deep learning for dynamic system identification

Zhou, H. (TU Delft Robot Dynamics)
Chahine, I. (Student TU Delft)
Zheng, Wei Xing (Western Sydney University)
Pan, W. (TU Delft Robot Dynamics; The University of Manchester)

2022

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 regularised optimisation procedure that can be solved as efficiently as training typical DNNs. Remarkably, an efficient and recursive Hessian calculation method for each layer of DNNs is developed, turning the intractable training/optimisation process into a tractable one. 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 system identification benchmarks by achieving good and competitive simulation accuracy. The code to reproduce the experimental results is open-sourced and available online.

Deep neural networks
Group sparsity
Regularised system identification
Sparse Bayesian learning

http://resolver.tudelft.nl/uuid:72ef293a-5e1b-478a-932c-ac7b900b669c

https://doi.org/10.1016/j.automatica.2022.110489

0005-1098

Automatica, 144

Institutional Repository

journal article

© 2022 H. Zhou, I. Chahine, Wei Xing Zheng, W. Pan