Regularized Parameter Identification in the Tumor Growth Model

This study addresses the inverse problem of parameter identification in mathematical models of tumor growth under limited and noisy experimental data. Three classical growth models—logistic, Richards, and Gompertz—are investigated in the context of structural and practical identifiability. It is demonstrated that, despite structural identifiability, parameter estimation remains highly unstable due to the ill-posed nature of the inverse problem. A comparative analysis of the Levenberg–Marquardt method and a genetic algorithm shows that improvements in optimization strategies alone do not resolve this instability and may lead to overfitting. To overcome this limitation, a Tikhonov regularization framework is introduced for the Gompertz model, ensuring stable and physically interpretable parameter estimates. The regularized formulation provides a balance between data fidelity and parameter stability, resulting in improved agreement with experimental observations. To further validate the identified parameters, a reaction–diffusion partial differential equation model is employed. Numerical simulations demonstrate that regularized parameters lead to significantly different spatial tumor morphologies, including more compact structures with sharper interfaces, highlighting the impact of inverse problem regularization on forward model predictions. The results confirm that the primary limitation in tumor growth modeling lies in the ill-posedness of the inverse problem rather than in the choice of optimization algorithm. The proposed framework provides a robust approach for parameter identification and improves the reliability of predictive tumor growth models.