Black-Box System Identification with Deep Recurrent Networks and Classical Models

Date

2026-2-20

Author

Avan, Beyza

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Deep learning has demonstrated significant, well-established success across a range of application domains; however, its use in nonlinear system identification remains an active area of research. This thesis provides a rigorous comparative analysis of Recurrent Neural Networks (RNNs) and classical identification frameworks for nonlinear black-box system identification on standard benchmarks. Specifically, recurrent neural architectures, including RNN, long short-term memory, and gated recurrent unit models, are compared against two classical identification baselines: a linear Box-Jenkins (BJ) model and a Nonlinear Autoregressive Model with eXogenous input (NARX). Performance is evaluated using various measures of prediction error alongside training time, to quantify the trade-off between predictive accuracy and efficiency. The comparative evaluation is conducted on the Silverbox benchmark system, a widely used reference for nonlinear system identification. Classical baselines are first established by tuning model orders, demonstrating that grid search improves BJ model performance relative to standard configurations. Subsequently, an RNN baseline, an RNN variant incorporating a correlation-guided lag selection procedure (both written from scratch), and a PyTorch-based RNN model driven solely by past input sequences are implemented to assess whether long memory windows are necessary or not. A specific contribution of this study is the design of correlation-guided modified RNN that replaces long sliding-window inputs with a compact set of informative lagged regressors. The results obtained from its application show that principled correlation-driven lag selection achieves superior predictive accuracy compared to both the RNN baseline and long-horizon architectures, while simultaneously reducing model complexity. To assess the transferability of the proposed lag-design principle, the correlation-guided modified RNN is further evaluated on the Wiener–Hammerstein benchmark, where a similarly compact set of informative lagged regressors is found to remain effective. Overall, the results indicate that embedding informative lagged regressors into RNNs provides an accurate and computationally efficient approach to nonlinear black-box system identification. In addition to input-only recurrent models, ARX-type RNN formulations that incorporate autoregressive output feedback alongside inputs are investigated. On the Silverbox benchmark, these ARX-type architectures achieve the strongest performance, highlighting the importance of explicit output feedback for capturing the underlying nonlinear dynamics.

Subject Keywords

System identification, Deep neural networks, Recurrent neural networks, Long short term memory, Gated recurrent units, Box-Jenkins model, ARX model

URI

https://hdl.handle.net/11511/118489

Collections

Graduate School of Applied Mathematics, Thesis