@article {352,
	title = {Investigation of Proper Orthogonal Decomposition for Echo State Networks},
	journal = {Neurocomputing},
	year = {2023},
	pages = {126395},
	abstract = {<p>Echo State Networks (ESN) are a type of Recurrent Neural Network that yields promising results in representing time series and nonlinear dynamic systems. Although they are equipped with a very efficient training procedure, Reservoir Computing strategies, such as the ESN, require high-order networks, i.e., many neurons, resulting in a large number of states that are magnitudes higher than the number of model inputs and outputs. A large number of states not only makes the time-step computation more costly but also may pose robustness issues, especially when applying ESNs to problems such as Model Predictive Control (MPC) and other optimal control problems. One way to circumvent this complexity issue is through Model Order Reduction strategies such as the Proper Orthogonal Decomposition (POD) and its variants (POD-DEIM), whereby we find an equivalent lower order representation to an already trained high dimension ESN. To this end, this work aims to investigate and analyze the performance of POD methods in Echo State Networks, evaluating their effectiveness through the Memory Capacity (MC) of the POD-reduced network compared to the original (full-order) ESN. We also perform experiments on two numerical case studies: a NARMA10 difference equation and an oil platform containing two wells and one riser. The results show that there is little loss of performance comparing the original ESN to a POD-reduced counterpart and that the performance of a POD-reduced ESN tends to be superior to a normal ESN of the same size. Also, the POD-reduced network achieves speedups of around 80\% compared to the original ESN.</p>},
	keywords = {Echo State Networks., Model Order Reduction, reservoir computing},
	issn = {0925-2312},
	doi = {https://doi.org/10.1016/j.neucom.2023.126395},
	url = {https://www.sciencedirect.com/science/article/pii/S0925231223005180},
	author = {Jean Panaioti Jordanou and Eric Aislan Antonelo and Eduardo Camponogara and Eduardo Gildin}
}
@article {337,
	title = {Echo State Networks for Practical Nonlinear Model Predictive Control of Unknown Dynamic Systems},
	journal = {IEEE Transactions on Neural Networks and Learning Systems},
	year = {2021},
	pages = {1-15},
	abstract = {<p>Nonlinear model predictive control (NMPC) of industrial processes is changeling in part because the model of the plant may not be completely known but also for being computationally demanding. This work proposes an extremely efficient reservoir computing (RC)-based control framework that speeds up the NMPC of processes. In this framework, while an echo state network (ESN) serves as the dynamic RC-based system model of a process, the practical nonlinear model predictive controller (PNMPC) simplifies NMPC by splitting the forced and the free responses of the trained ESN, yielding the so-called ESN-PNMPC architecture. While the free response is generated by the forward simulation of the ESN model, the forced response is obtained by a fast and recursive calculation of the input-output sensitivities from the ESN. The efficiency not only results from the fast training inherited by RC but also from a computationally cheap control action given by the aforementioned novel recursive formulation and the computation in the reduced dimension space of input and output signals. The resulting architecture, equipped with a correction filter, is robust to unforeseen disturbances. The potential of the ESN-PNMPC is shown by application to the control of the four-tank system and an oil production platform, outperforming the predictive approach with a long-short term memory (LSTM) model, two standard linear control algorithms, and approximate predictive control.</p>},
	keywords = {Echo State Networks, Model Predictive Control, reservoir computing},
	doi = {10.1109/TNNLS.2021.3136357},
	url = {https://ieeexplore.ieee.org/abstract/document/9664461},
	author = {Jordanou, Jean Panaioti and Antonelo, Eric Aislan and Camponogara, Eduardo}
}
