Physics-informed neural network approach for analyzing the dynamics of uterine leiomyosarcoma through fractional modeling

Abstract This study presents a mathematical model of Uterine leiomyosarcoma where the system of equations are framed using Atangana–Baleanu–Caputo fractional derivative to establish memory effects in disease evolution. The well-posedness of the model is ascertained through analytical results. Numerical simulations are conducted with different fractional orders to analyze the influence of memory on progess of the disease. Analysis of optimal control was established along with numerical results. We utilize a physics informed neural network governed by the fractional differential equations to enhance predictive accuracy. The neural network is trained on clinical data spanned over an average period of 250 months with Adam’s optimizer and rigorously learns the compartmental dynamics and transition parameters, yielding a stable convergence and low loss function value of 10 ⁻² . The proposed dual approach of fractional modeling and computational physics-informed neural network framework establishes a systematic way for analyzing the disease dynamics effectively.