Machine Learning & Data Science in Optimization
Saeed Mirzajani; Majid Roohi
Abstract
The prediction of chaotic time series is essential for understanding highly nonlinear and sensitive systems, with the Lorenz system serving as a standard benchmark due to its intricate and non-periodic dynamics. Classical forecasting approaches often struggle to capture such irregularities, ...
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The prediction of chaotic time series is essential for understanding highly nonlinear and sensitive systems, with the Lorenz system serving as a standard benchmark due to its intricate and non-periodic dynamics. Classical forecasting approaches often struggle to capture such irregularities, motivating a shift toward deep learning–based strategies. In this study, we develop two hybrid models—Feedback Long Short-Term Memory (FB-LSTM) and Feedback Variational Stacked LSTM (FBVS-LSTM), specifically designed for multivariate prediction of the Lorenz system. By embedding feedback structures into LSTM networks, the proposed methods deliver enhanced short-term prediction performance without substantial computational costs. Comparative simulations indicate that our frameworks surpass traditional RNNs and baseline LSTM models, achieving prediction accuracies up to 94%. These findings indicate that feedback-enhanced architectures offer effective and practical tools for forecasting chaotic systems, with potential applications in both scientific research and engineering practice.
Majid Roohi; Mohammad Pourmahmood Aghababa; Javid Ziaei; Chongqi Zhang
Abstract
The present study introduces a kind of fractional-order Hopfield neural network (FOHNN), and its complex dynamic behavior is investigated through chaos analyses. With the use of phase space analysis and bifurcation diagrams and maximal Lyapunov exponent (MLE) it is demonstrated that ...
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The present study introduces a kind of fractional-order Hopfield neural network (FOHNN), and its complex dynamic behavior is investigated through chaos analyses. With the use of phase space analysis and bifurcation diagrams and maximal Lyapunov exponent (MLE) it is demonstrated that for the values of 0.87 < α < 1, as the fractional-order (FO), the dynamical behavior of the mentioned FOHNN is chaotic. Then, the bounded trait of chaotic systems is utilized to derive an adaptive model-free control technique to suppress of complex dynamics of the FOHNN. Furthermore, according to the matrix analysis theorem of non-integer-order systems and the adaptive model-free control methodology, analytical consequences of the designed controller are evidenced. Eventually, two examples are reported to illustrate the applicability of the mentioned model-free control method.
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