NONE 20260715104223297 wseas/wseas content-registration-form@crossref.org content-registration-form International Journal of Applied Mathematics Computational Science and Systems Engineering 2766-9823 Allag Fateh Harrag Abdelmalek Fenni Mohamed Bounechada Mustapha Chaotic systems exhibit sensitivity to initial conditions and external parameters, posing challenges for long-term prediction. This study investigates the capability of deep neural networks (DNNs) to infer the time-evolution of the Rössler system a canonical chaotic oscillator by leveraging initial conditions (x0,y0,z0) and forcing parameters (a,b,c) as input variables. A 3D convolutional neural network (3D-CNN) architecture is designed to map these inputs to future states of the system. Results demonstrate that the DNN achieves high accuracy in short-term predictions (<50 time units) but faces exponential error growth beyond this horizon due to chaos. Notably, parameter variations (a,b,c) induce systematic shifts in attractor topology, while initial conditions amplify prediction uncertainty. The study highlights DNNs as viable tools for short-term chaotic forecasting but underscores the need for hybrid approaches to address long-term instability. 07 15 2026 07 15 2026 80 7 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/232026.2026.8.7 https://wseas.com/journals/amcse/2026/a14amcse-007(2026).pdf Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130–141. Rössler, O. E. (1976). An equation for continuous chaos. Physics Letters A, 57(5), 397–398. Pathak, J., Wikner, A., Fussell, D., Chandra, S., Hunt, B. R., Girvan, M., & Ott, E. (2017). Hybrid data-model approaches for chaos. Journal of Computational Physics, 354, 413– 438. Sprott, J. C. (2001). A simple chaotic flow. Chaos: An Interdisciplinary Journal of Nonlinear Science, 11(2), 309–316. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686– 707. Ott, E., Grebogi, C., & Yorke, J. A. (2018). Controlling chaos. Physics Today, 41(5), 46– 53. Pathak, J., Hunt, B., Girvan, M., Lu, Z., & Ott, E. (2018). Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach. Physical Review Letters, 120(2), 024102. Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning. MIT Press. LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. *Nature*, 521(7553), 436– 444. Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285– 317. prediction. Journal of Thermal Analysis and Calorimetry, 145, 2191–2207.