Supervised AdamW Optimizer Based Guided Physics Informed Neural Network for Sigmoid Controlled Variable Fractional System: Hyperchaos in Electrical Circuits

In this article a robust Guided Physics-Informed Neural Network (GPINNs) method is used for learning and predicting the nonlinear dynamic of variable-order fractional hyperchaotic mathematical model. Fractional orders are based on polynomial, trigonometric and hyperbolic function into the sigmoid function. This variable-order fractional hyperchaotic system has been solved with GPINNs scheme that integrates data-driven learning with physics-based constraints. Four distinct fractional-order scenarios are considered to capture a broad range of memory and hereditary effects, that are inherent in practical electronic circuits. These cases made comprehensive assessment of the ability of the model. Furthermore, the effectiveness of this approach is shown through detailed analyses of time-series evolution, phase-space projections, and training diagnostics for multiple control parameters. This framework also highlights the strong potential of GPINNs for modeling complex integer- and variable fractional-order hyperchaotic systems, with promising applications in electronic circuit design, secure communication, and advanced signal processing.