Predicting the Effect of Chemotherapy on the State of a Cancerous Tumor Using Fractal-Physical-Information Neural Networks

Understanding tumor dynamics under chemotherapy is important for improving the prediction of cancer progression and assessing treatment effectiveness. This paper proposes a numerical modeling approach based on a fractal physics-informed neural network (fPINN) designed to solve nonlinear fractional-order differential equations describing the interaction of cell populations during cancer therapy. The mathematical model is formulated using the Atangana–Baleanu fractional operator in the Caputo sense, which makes it possible to capture both the fractal structure and hereditary properties of biological systems. The proposed architecture consists of four independent neural networks modeling the concentrations of stem cells, effector cells, tumor cells, and the chemotherapeutic agent. Model training is performed using a hybrid loss function that combines the residuals of the governing equations, initial conditions, and reference data generated by the Atangana–Toufik numerical method. The experimental results demonstrate high model accuracy, particularly for components with complex nonlinear dynamics. These findings indicate that the proposed fPINN framework is a promising tool for predicting tumor evolution and analyzing the impact of chemotherapy.