Open Access

ARTICLE

FPGA Implementation of a Multilayer Perceptron for the Reconstruction of Chaotic Time Series

Omar Guillén-Fernández¹, Carlos Alejandro Velázquez-Morales¹, Luis Gerardo de la Fraga², Sajad Jafari^3,4, Esteban Tlelo-Cuautle^1,*

1 Department of Electronics, Instituto Nacional de Astrofísica, Optica y Electrónica, Puebla, Mexico
2 Computer Science Department, CINVESTAV, Mexico City, Mexico
3 Center for Research, Easwari Engineering College, Chennai, India
4 Center for Cognitive Science, Trichy SRM Medical College Hospital and Research Center, Trichy, India

* Corresponding Author: Esteban Tlelo-Cuautle. Email:

(This article belongs to the Special Issue: Computational Modeling, Simulation, and Algorithmic Methods for Dynamical Systems)

Computer Modeling in Engineering & Sciences 2026, 148(3), 29 https://doi.org/10.32604/cmes.2026.086260

Received 27 May 2026; Accepted 04 September 2026; Issue published 28 September 2026

Abstract

The reconstruction of chaotic time series can be considered fundamental for modeling nonlinear dynamical systems and enabling real-time processing applications. However, their hardware implementation remains challenging due to the inherent complexity and high sensitivity to initial conditions exhibited by chaotic systems. The proposed work shows that artificial neural networks based on multilayer perceptrons (MLPs) provide an efficient approach for approximating nonlinear dynamics and are well suited for implementation on reconfigurable hardware platforms such as Field Programmable Gate Arrays (FPGAs). In this manner, an MLP is trained in software using Python and the scikit-learn library to model the dynamics of the Lorenz, Chen, and Rössler chaotic systems. The trained network is subsequently implemented on an FPGA Cyclone IV GX SoC DE2i-150 EP4CGX150DF31C7 using Verilog Hardware Description Language (Verilog-HDL). The proposed work shows the digital block diagram descriptions of the MLPs for the reconstruction of Lorenz, Chen, and Rössler chaotic attractors, which consist of multiplexers, matrix multipliers, adders, Parallel-In Parallel-Out (PIPO) registers, ROM (Read-Only Memory) and RAM (Random Access Memory), and a control unit. In addition, a Rectified Linear Unit (ReLU) block is used to approximate the activation function. The FPGA hardware resources are given for the experimental observations of each reconstructed chaotic attractor, which are in good agreement with theoretical simulation results. With the data generated by the three MLPs that model each chaotic system, three pseudo-random number generators (PRNGs) have been constructed, whose randomness is verified by performing TestU01 and NIST tests. The FPGA implementation demonstrates that the proposed MLP architectures successfully reconstruct the chaotic time series with high accuracy, validating the feasibility of implementing neural network models in hardware for efficient modeling and real-time study of nonlinear dynamical systems.

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