Embedded deep reservoir computing for modelling complex industrial systems

Industrial processes are becoming increasingly complex, requiring advanced modelling techniques to understand their behaviour and improve their performance. In this context, deep learning algorithms have proven to be effective tools for modelling dynamic systems, with Recurrent Neural Networks (RNNs) being particularly suitable for time-series data. However, the computational complexity of deep learning models can be a limitation in industrial environments, where real-time responses are required. This work proposes the use of Deep Echo State Networks to model an industrial system. The aim is to evaluate its performance in real-time industrial applications when running on embedded devices. The approach is validated on a process composed of four interconnected water tanks, which exhibits typical nonlinear industrial dynamics. Among several candidate architectures (including vanilla RNNs or LSTMs), Deep ESNs were selected for their balance of accuracy and computational efficiency. Different input-output setups and number of Deep ESN layers are tested, and results are compared with LSTMs in terms of accuracy and execution time. Finally, the best Deep ESN models are implemented on industrial embedded devices to evaluate the possibility of running these models in real time. The proposed approach achieved up to a 33% reduction in RMSE and a 14% improvement in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> compared to traditional reservoir computing, highlighting its superior predictive performance. The results show that Deep ESN models can effectively model the industrial system, with the best configurations achieving high accuracy and low execution times, demonstrating the feasibility of running these models in real time in industrial environments.