2021/04/20 by Dario Piga, Marco Forgione, Piga, Dario +3 · 1 citation
Computer Science · Physics and Astronomy · Engineering · #Neural Networks and Applications #Model Reduction and Neural Networks #Control Systems and Identification
paper · pdf · doi:10.48550/arxiv.2104.09839
This paper presents a linear dynamical operator described in terms of a\nrational transfer function, endowed with a well-defined and efficient\nback-propagation behavior for automatic derivatives computation. The operator\nenables end-to-end training of structured networks containing linear transfer\nfunctions and other differentiable units by exploiting standard deep learning\nsoftware.\n Two relevant applications of the operator in system identification are\npresented. The first one consists in the integration of prediction error\nmethods in deep learning. The dynamical operator is included as the last\nlayer of a neural network in order to obtain the optimal one-step-ahead\nprediction error.\n The second one considers identification of general block-oriented models from\nquantized data. These block-oriented models are constructed by combining linear\ndynamical operators with static nonlinearities described as standard\nfeed-forward neural networks. A custom loss function corresponding to the\nlog-likelihood of quantized output observations is defined. For gradient-based\noptimization, the derivatives of the log-likelihood are computed by applying\nthe back-propagation algorithm through the whole network. Two system\nidentification benchmarks are used to show the effectiveness of the proposed\nmethodologies.\n