Supervised autoregressive eXogenous Networks with Fractional Grünwald–Letnikov finite differences: Tumor Evolution and Immune Responses under Therapeutic Influence fractals model

Abstract

Modeling malignant disease with immune retorts under therapeutic influence using fractional calculus and recurrent time-delay neural networks is an innovative approach that combines mathematical modeling with machine learning techniques to model inherent complexity of tumor behavior and forecasting of accurate therapeutic dosing timeline. Fractional aspect captures the memory effect of multifaceted tumor cells growth and artificial intelligence predicts treatment methodology such as drug dosing and help doctors to develop more effective and targeted treatments. This study develops a highly reliable and precise application of artificial intelligence-based methodology that utilize the insights, derived from fractional calculus to predict the tumor immune response to treatment, including optimal timing and drug dosing strategies. The utilization of recurrent time-delay neural networks in modeling malignant disease emerges as a beacon of innovation and computational sophistication. Grünwald–Letnikov (GL) based fractional solver is used to generate the synthetic data set for training, validation and testing of the designed neural networks methodology. To ascertain the genuineness and performance of the designed framework, a rigorous error analysis of different cases was performed. The accuracy and performance of the framework are further achieved in term of mean square error, meticulously optimized through iterative learning, regression metrics, cross-correlation, autocorrelation and histogram analysis.